I found something that bears on this. Unidentified southern irregulars ambushed elements of Colonel Nicholas Perczel's 10th Iowa Infantry Regiment at or near Charleston, Misissippi County, MO on 7 January 1862. The Rebels pulled back when the remaining Iowans fired back, but the 10th lost 5 killed outright, 2 mortally WIA, and 15 others wounded less than mortally. Sources for this include the 1975 history of Mississippi County, pp. 239-40 and "Official Records" series 1, vol. 8, pp. 47-8.
I would imagine the southerners took the flag from Charleston at that time.