I had long suspected this regiment (10th Wisconsin Infantry Regiment) lost a flag or both colors at the battle of Chickamauga (Day two). They had 145 (Captured) certainly a red flag. The 10th Wisconsin was in Colonel Scribner's brigade (one of the last brigades to pull out of Kelly's field.)
I finally found a source, (The Maps Of Chickamauga) David A. Powell (Author).
Page 246 states:
"Private August Bratnober described the scene in the 10th Wisconsin, suddenly we were charged from the right where we supposed our troops were...we gave way and made our best for the rear, only to discover we were completely surrounded. It was everyone for himself by this time, Bratnober followed the regimental colors toward what he thought was escape, but both he and the colors were soon in enemy hands."
Mr. Powell's Source: "Extracts from the August Bratnober Diary, 10th Wisconsin File, CCNMP."
Brigadier-General Lucius E. Polk's brigade formation (Left to Right) 3/5 CSA---1st Ark--2 TN--48th TN--35th TN.
Thus, the 35th Tennessee was on the right of the brigade and they were closest to the 10th Wisconsin (Right flank and rear).
Have a good morning,