I found a Col. William S. Brooks of the 56th U.S.C. (3rd Arkansas Infantry), from St. Louis MS, who was killed at Big Creek AK. His regiment was engaged with Gen. Dobbins.
Just a guess -- the flag and cuff could have been sent home in honor of Brooks.
Name: William Brooks
RESIDENCE: Mount Pleasant, Iowa
Enlistment Date: 23 Apr 1861
Side Served: Union
State Served: Iowa
Service Record: Enlisted as a Private on 23 April 1861 at the age of 21.
Enlisted in Company F, 1st Infantry Regiment Iowa on 14 May 1861.
Mustered Out Company F, 1st Infantry Regiment Iowa on 21 Aug 1861 at St Louis, MO.
Promoted to Full 2nd Lieutenant (As of Co. D 19th IA Infantry) on 20 Aug 1862.
Commission in Company D, 19th Infantry Regiment Iowa on 20 Aug 1862.
Promoted to Full Captain on 13 Mar 1863.
Promoted to Full Lieutenant Colonel (As of 56th USCT Infantry) on 7 Jul 1863.
Discharged for promotion Company D, 19th Infantry Regiment Iowa on 7 Jul 1863.
Commission in Company S, 56th Infantry Regiment U.S. Colored Troops on 7 Jul 1863.
Promoted to Full Colonel (Estimated date) on 1 Apr 1864.
Killed Company S, 56th Infantry Regiment U.S. Colored Troops on 26 Jul 1864 at Wallace's Ferry, AR.
More research is definitely needed.