I don't have time tonight to do more research for you but here is Kershaw's report from Chicamauga. I would not be surprised if the Regts. didn't submit reports. They lost a lot of senior leadership at Chicamauga and had months of hard campaigning ahead.

I don't have time to jump in the whole Jenkins/Law debate. Both being Citadel men, as are all Citadel men, were excellent leaders. ;^). Please remember their relationship goes back to before the war when Law worked for Jenkins. That working relationship did not go well and carried into their careers in the ANV. Jenkins ranked Law and had already be recommended for divisional command and a second star prior to Chicamauga. Law was guility of of misconduct in battle for failing to support his commanding officer (Jenkins) on at least two occassions (Lookout Mountain and Knoxville I believe). He also politiced to get Longstreet dismissed from the service.

HEADQUARTERS KERSHAW'S BRIGADE,

Near Chattanooga, October 15, 1863.
MAJOR: I respectfully submit the following report of the operations of my own and Humphreys' brigades in the late battle of Chickamauga. The mention of the latter brigade is necessarily general from the fact that General Humphreys' report did not pass through me, and being on foot during the engagement, I could only assume a very general command. I respectfully refer to the report of General Humphreys for more particular information of his movements.
At midnight on September 18, the last of my brigade arrived at the terminus of the railroad near Catoosa Station, and next morning marched, under orders from the general commanding, to Ringgold, at which place the command united with that of Brigadier-General Humphreys.
About nightfall orders were received from the lieutenant-general commanding to join General Hood with the command, conducted by Colonel Dilland [?]. We moved at once across Alexander's Bridge, over Chickamauga, and bivouacked at 1 a.m. on the 20th.
At 9 o'clock we were ordered by the lieutenant-general commanding to a position in reserve to Hood's division, near the headquarters of the commanding general.
About 11 o'clock I was ordered forward with the command to report to Major-General Hood. Arriving, I found his troops engaged in front and a line of battle just going in. General Hood directed me to form line in his rear, with my center resting on the spot where I found him, which, I suppose, was his center. Forming line (Humphreys on my left) as rapidly as possible under fire of the enemy and in a thick wood, I moved, as directed, to the front. I had been directed to occupy a line of breastworks, but before reaching that point a staff officer of the lieutenant-general commanding was sent to direct me to a point farther in advance. I crossed the La Fayette road near a house, and, crossing the open ground, entered the woods beyond and proceeded nearly to what I understood to be the Cove road. While passing through the last wood Lieutenant-General Longstreet directed me to look out for my right flank, and I had disposed of Colonel Henagan's Eighth South Carolina, my right regiment, in such a manner as to cover me in that direction, as I supposed.
Having reached the point last mentioned, the firing on my right became very heavy, and a portion of General Hood’s division fell back along my line. I changed front almost perpendicularly to the right on Colonel Nance's Third South Carolina Regiment, my left center, which I had indicated as the directing battalion. This movement had just been accomplished when an officer of Brigadier-General Law's staff informed me of the unfortunate loss of Major-General Hood, and suggested that as senior brigadier I should assume the direction of the two brigades of that division on my right. General Bushrod R. Johnson was present, and called for a comparison of rank, which seemed to satisfy him. Major Cunningham, assistant inspector-general, General Hood's staff, who had been sent by the general to conduct me, made the opportune suggestion that the lieutenant-general commanding be informed. Relieved by this, I requested him to direct General Humphreys to move up and support me on my right, he having been thrown in my rear by my change of front. General Johnson had undertaken to advance a brigade on my left. The enemy occupied a skirt of wood on the farther side of the field around Dyer's house, his right extending into the wood beyond the field, his left crossing the Cove road. His colors were ostentatiously displayed along the lines.
The last of Hood's division engaged in my front had just retired when I ordered the advance, directing Colonel Henagan to extend to the right and engage the enemy in that direction until Humphreys' arrival, who was then in motion. The distance across the field was about 800 yards, with a fence intervening about one-fourth of the distance. As soon as we crossed the fence, I ordered bayonets fixed, and moved at a double-quick, sending Lieutenant-Colonel Gaillard, Second South Carolina Regiment (my extreme left), to gain the enemy's right flank.
When within 100 yards of the enemy they broke, and I opened fire upon them along the whole line, but pursued them rapidly over the first line of hills to the foot of the second, when I halted under a heavy fire of artillery on the heights, sheltering the men as much as possible, and there awaited the coming of Humphreys, on my right. My Seventh South Carolina, Lieutenant-Colonel Bland, my right-center regiment, and Fifteenth South Carolina Regiment, Lieut. Col. Joseph F. Gist, had obliqued to the right. Colonel Henagan had pursued the enemy so far to the right that when Humphreys got up he occupied the interval between the Fifteenth and Eighth Regiments.
Colonel Oates, Fifteenth Alabama, Law's brigade, came up on the right of the Seventh, and occupied the line between that and the Fifteenth, and, with those regiments, advanced without orders. I had sent to the right to direct that I should be informed when Humphreys arrived. Hearing the firing renewed on my right, I advanced the left wing (Third South Carolina, James battalion, and Second South Carolina) and gained in some points the crest of the hill within a few yards of the enemy's lines.
After one of the most gallant struggles I have ever witnessed, especially on the part of the Third South Carolina and James' battalion, which occupied a position in front of the enemy's battery, I was compelled to fall back to a point about 250 yards back, where I determined to hold the enemy until re-enforcements arrived. The enemy soon advanced, but by a cool, deliberate fire were quickly repulsed. General Humphreys reported that he could make no farther advance on account of the heavy force of the enemy to his right. I directed him to make such disposition of his troops as would cover my right flank.
About 3 o'clock Brigadier-General Anderson's Mississippi brigade came to my support. I described to him the situation, and suggested an attack on the right flank of the position of the enemy. He acquiesced in my view, and advanced his left preparatory to the movement, covering his front with skirmishers, who immediately became engaged, and drove in those of the enemy; but, raising a shout along their line, they advanced their line of battle at a charge, driving back Anderson's brigade in some confusion. With hearty cheers, the Second and Third South Carolina and James' battalion engaged with the utmost enthusiasm. Anderson's brigade promptly reformed and opened fire. His reserve regiment came up, and in ten minutes' time the enemy was driven pell-mell. The Second South Carolina and Anderson's brigade dashed after him and drove him to the top of the hill, the Second South Carolina reaching the crest. The troops to his left having fallen back to their former position, Lieutenant-Colonel Gaillard says in his report" that he was obliged reluctantly to fall back. This was an attack on right flank of the enemy, and the line was at an oblique angle to my line. All of my regiments, except the Second; though not participating in the direct attack, served to hold the enemy in position along that portion of the line, and were mostly engaged during the attack.
About 4 o'clock Gracie's and Kelly's brigades came up and reported to me. I directed them, the former to form on my rear and the latter to form on Gracie's left. General Hindman informed me that he was about to attack on Anderson's left, well on the right flank of the enemy, with two brigades of infantry with artillery. Soon after he opened heavily in that direction, but sent me word the-attack was likely to fail unless a demonstration was made along the front. I determined on an attack, combining all our forces; Mc-Nair's brigade, which had come up, on my right, Gracie's, Kelly's, Anderson's, my own, Eighth, Fifteenth, and Second Regiments participating. The rest of my brigade, being in whole or in part out of ammunition, remained in reserve at their position. This was one of the heaviest attacks of the war on a single point. The brigades went in magnificent order. General Gracie, under my own eye, led his brigade, now for the first time under fire, most gallantly and efficiently, and for more than an hour and a half the struggle continued with unabated fury. It terminated at sunset, the Second South Carolina being among the last to retire.
At dark General Robertson, of Hood's division, came up with his brigade and picketed to my front. About 10 o'clock, I think, he informed me that the enemy had left. I immediately communicated the fact to the lieutenant-general commanding.
In the morning General Robertson withdrew, and I sent forward Lieutenant-Colonel Gaillard to take possession of the enemy's hospital and to picket to the front. The day was spent in caring for the wounded, burying the dead, and collecting arms.
In the afternoon Major-General McLaws resumed command of the division. My brigade was marched a few miles that night toward Chattanooga and next day drove in the enemy to their present lines, in conjunction with Wofford's brigade, my eighth South Carolina being chiefly engaged. But few men were lost in this affair.
During the first charge of the 20th my brigade captured nine pieces of artillery, three of which were taken by the Eighth South Carolina, and some half dozen caissons, with ammunition. Most of these were taken before they could open fire.
My losses were heavy, as will be seen by reference to the accompanying detailed report. Among them are some of the most gallant and efficient officers and men of my command and choice spirits of Carolina chivalry.
Lieut. Col. Elbert Bland, Seventh South Carolina, fell at the head of his regiment in the first moment of our triumph. A few moments later Maj. John S. Hard, his successor, was instantly killed. The command then devolved on Capt. E. J. Goggans. Capt. J. M. Townsend, commanding James' battalion, was killed leading the charge upon the enemy's stronghold. Lieutenant-Colonel Hoole, Eighth South Carolina Regiment, was killed in the early part of the action.
Lieutenant-Colonel Bland was recognized generally as an officer of rare ability. His power of command; his cool, dauntless courage and self-control in battle; his excellent judgment and disciplinary skill and ability in camp marked him as a man of a high order of military talent. His personal and social characteristics were equally noble and elevated. In him we have lost a champion worthy of our glorious cause.
Maj. John S. Hard was a gallant and accomplished officer, and has highly distinguished himself on every battlefield in which his regiment has been engaged.
Captain Townsend commanded his battalion on this occasion in such a manner as to elicit my commendation on the field before he fell, and would if he were living have been here mentioned with high distinction.
Lieutenant-Colonel Hoole was an officer of much merit, but has been prevented by protracted illness from attaining that distinction he might have achieved with his gallant regiment. He was much beloved for his personal qualities, and his loss will be deeply deplored by his comrades.
For particular mention of other brave spirits who have fallen, I respectfully refer to the accompanying reports of regimental commanders. My pride and satisfaction with the conduct of my entire brigade in the engagement could not be more complete. Officers and men each acted as if impressed with the feeling that the destinies of the country depended upon his own faithful, earnest, and intelligent discharge of duty. I shall not attempt to particularize.
The only member of my staff with me during the whole day was Capt. C. R. Holmes, assistant adjutant-general. To him, as on all previous occasions of this character, I am greatly indebted for the most valuable and gallant services. He represented me on the right wing of my brigade.
I detailed Second Lieut. H. L. Farley to act as aide-de-camp, and cannot too highly commend his gallantry, activity, and efficiency under the most trying circumstances. As an evidence of my appreciation I detailed him to accompany the captured flags to Richmond.
Lieut. W. M. Dwight, assistant adjutant and inspector general, joined me in the afternoon, and aided me with his usual efficiency.
In the absence of horses for myself and staff, I detailed one man from each regiment as orderlies to communicate with the command. All of them rendered efficient service, and two (M. F. Milam, Company A, Third South Carolina Regiment, and Rawlins Rivers, Company I, Second South Carolina Regiment) were killed in discharge of that duty. Rivers had attracted my notice by gallant and intelligent services in the same position at the battle of Fredericksburg.
I have the honor to be, major, very respectfully, your obedient servant,
J. B. Kershaw
Brigadier-General, Commanding.
Maj. JAMES M. GOGGIN,
Assistant Adjutant-General.
[Inclosure.]
Report of Casualties in Kershaw's brigade.
Officers and men. Killed. Wounded. Missing. Total
Officers. 9 38 .... 47
Enlisted men 56 400 1 457
Total 65 438 1 504
Number of prisoners taken by brigade 346
Number of stands of arms. 1,014