I'm pretty sure that's him. Still confirming some details but Capt. Harrison Dearborn Flowers was apparently know as "Judge Flowers". He was enrolled by Dawson though he doesn't appear in Dawson's 19th AR. He was the second captain of Co. A, 24th AR Inf, elected in August 1862, following Levi Mitchell. His enlistment in April was right before the events near Eagletown, Choctaw Nation. About a month later, Dawson is ordered to Little Rock. I found on a genealogy site the statement that in 1863, Flowers was headed home to visit his family in Sevier County and was shot in the back and killed in Hot Springs County. The source given for this is The Autobiography of Henry Merrell.

Ken