Shawn,
This capture has been attributed to the presentation Second National flag of the 11th Tennessee Infantry. I have also seen it as being captured at Franklin by the 118th Illinois - who was not there!
The 108th Illinois was not in the Atlanta or Tennessee campaigns of 1864 and neither was the 188th Illinois according to Dyer's Compendium.
This one was found somewhere, probably in or around Dalton, GA in 1864 after that town fell to Sherman and was sent to Illinois by whatever Illinois unit took it. It was then sent to Tennessee well after the war as these newspaper accounts state - but with the wrong capturing units.
greg Biggs