Well I have found the Confederate regiment that captured the 21st Wisconsin's flag at Chickamauga. This was almost too easy.
From the micro film of the "War Department Returned Battle Flags" 1905. They had listed the 21st Wisconsin losing a flag at Chickamuaga to the "1st Mississippi". As we all know that regiment was not at Chickamauga. The micro film even said "Humphrey's Brigade, Mclane's division, Longstreet's Corps." You can see the spelled McLaw's name wrong.
So I took the name of W.H. Barnett who had captured the 21st Wisconsin's flag, he was in Company A and a Sergeant.
So I checked the National Archives, soldier/sailor website system.
I typed in Barnett--last name, W--first name, then Mississippi Infantry. 16 names came up. Then I looked at the names with "W.H.Barnett" sure enough in the 21st Mississippi there was a "W.H.Barnett" Company A and he was a sergeant.
So, the 21st Wisconsin lost a flag at Chickamauga to the 21st Mississippi. Humphrey's brigade claims to have captured 5 flags. This is the only flag I know of, so far.
One more down...
Have a great weekend,