I did find a reference to the John F. Reynolds GAR Camp in Cullman, Alabama. It may have been named in honor of General John Fulton Reynolds who was killed at the first day of Gettysburg. As your probably aware of the GAR Posts usually kept a roster of members. Have you checked with the ADAH to see if they have anything on this camp? You may also want to check with the Cullman County Historical Society if they have one? What was your grandfather name? You mentioned if I remember correctly that your soldier in question was your great great grandfather. Blount County as you aware had many folks with the surname as Allred and various surname spellings. Blount County was also a part of Cullman County at one time. I did see a turn of the century photograph of an Allred family in Blount County, but did not see your ancestor mentioned.

JOHN FULTON REYNOLDS

Reynolds, John F., major-general, was born in Lancaster,
Pa., in 1820, graduated at West Point on July 1, 1841, and on
Oct. 23 following, received his commission as second lieutenant
in the 3d artillery. On June 13, 1846, he was promoted to the
rank of first lieutenant, and served throughout the Mexican
war, winning the brevets of captain and major for his "gallant and
meritorious conduct" at Monterey and Buena Vista. After his return from
Mexico he was engaged in military service in California, and against the
Indians on the Pacific coast. In 1852 he was appointed aid to Gen.
Wool, and on March 3, 1855, was promoted to a captaincy in the 3d
artillery. On May 14, 1861, he was appointed lieutenant-colonel of the
14th U. S. infantry, and on Aug 20 was commissioned brigadier-general of
volunteers, and appointed to the command of the 1st brigade of the
Pennsylvania reserve corps. In June, 1862, the reserves joined the Army
of the Potomac, on the peninsula, and Gen. Reynolds, on June 26,
participated in the battle of Mechanicsville, and the next day took part
in the severe battle of Gaines' Mill. He was also engaged at Savage
Station, and at Charles City cross-roads, where he took command of the
division after Gen. McCall was taken prisoner, and at a late hour the
same day was himself captured by the enemy and sent to Richmond. For
his gallantry in these battles he received the brevets of colonel and
brigadier-general in the regular army. After his release from Richmond,
on Sept. 26, he returned to the command of his division, and soon
after assumed command of the 1st army corps, by virtue of seniority of
rank. He commanded this corps in the first battle of Fredericksburg,
and in Jan., 1863, he was nominated major-general of volunteers. He
hastened forward in the movement to Gettysburg at the direction of the
commanding general, and arrived there in the vanguard of the Federal
army, and while bringing up the 2nd WI Infantry, he was shot from his
horse and killed instantly, July 1, 1863.

Source: The Union Army, vol. 8