I just found a paper, The Battle of Marion, December 17 and 18, 1864, written by David Chaltas and Richard Brown.
In the description of the battle is the sentence:
"Breckinridge's front regiment was the 10th Kentucky Mounted Rifles, under the command of Colonel Benjamin Caudill. The regiment rode under a blue flag with a white cross with the name 'Caudill's Army' stenciled across it."
I note that Caudill was a Minister.
I question whether this flag has ever been identified.