As far as I know, none of the Alabama Infantry Regiments of Battle's Brigade lost their flag at Fisher Hill. In fact, as noted in the following battle summary, Battle's Brigade came off the field intact. I believe your best candidates for loosing their flag on the Confederate side would be with members of Lomax's Cavalry or Cox's Brigade.

"At about 4:00 – 4:30 P.M., as the sun began to set behind Little North Mountain, Union General Crook’s two divisions, about 5500 strong, struck the Confederate left. The cavalry pickets put up no resistance and took to their heels, telling their comrades in Ramseur’s Division as they rushed by, that they had been flanked. In fact, a cavalryman continued down the line reporting to each command that they had been flanked on the left. This started a general panic in the line.

By the time Crook’s men reached Battle’s Brigade, the Union VI Corps on the Rebel front had connected with Crook’s left and the whole Union Army pressed forward from the left and front. General Ramseur desperately tried to hold his tenuous position by ordering Battle’s Brigade to reform facing left and sent Major Thomas J. Kirkpatrick’s Amherst Battery to their support. As the attackers rushed forward, the Confederate Battery fired canister into them and General Battle, wielding a cedar fence stake, urged his men to stand firm and shouted, “Close up! On your life!” This staunch resistance by the regiments of Battle’s Brigade and Kirkpatrick’s Artillery was later noted by Crook in his report. “On a prominent ridge about one mile from the base of the mountain where one of their main batteries was posted, the enemy made his most stubborn stand.” General Ramseur sent General Cox’s Brigade to their support, but the rest of the Confederate line was giving way and in the confusion, Cox got off track and left the Alabamian’s to fend for themselves.

The men continued to fight on. Finally, when the pressure of Crook’s attack became too much to endure, the Artilleryman raised his cap and said, “I thank you, gentlemen; it is useless to stay longer.” With that the guns and Battle’s Brigade withdrew from the field. An hour earlier, at about 5:00 P.M., Commissary Clerk, Henry Beck had been about to start forward to the Brigade with rations when he suddenly met the whole army running back, a stampede he compared to that of Winchester. “The Yankees flanked us by the mountain & got in our rear, which caused our cavalry to give away & cause confusion among the troops, when everybody put out the best way they could. We made a hasty retreat to Mt. Jackson, after traveling all night. Our loss here in men was not severe, we lost some 10 or 20 pcs. of artillery however.
Although the Confederate Army was routed, many histories have stated that not a single Division, Brigade or Regiment preserved its’ organization, however, this is not true. The Army’s Topographical Engineer, Jed Hotchkiss, would write in his journal, “...The artillery was open on the woods when the enemy was advancing and it check them for the moment, but most of our men went on, officers and all, at breakneck speed. Battle’s Brigade moved to the left and came out intact.” Major Eugene Blackford had in fact, drawn together some of his best sharpshooters along with the 5th and 6th Alabama Infantry Regiments and managed to provide enough of a rear guard to keep the Yankees at bay, allowing the rest of the Confederate Army to escape southward. Sheridan’s army pursued the Confederates south towards Woodstock, but stooped at Tom’s Brook, unable to finish them off."