The 32nd Alabama did lose their colors at Lavergne, TN in October, 1862. I do not think the flag in the Illinois National Guard Museum is that flag however. It is too large for a unit flag for one and the Union accounts state that two flags were taken if I correctly recall. The larger flag was probably a post flag for the encampment.
Where the 32nd Alabama flag is today I have no clue.
If you can get a copy of Howard Madaus' book on flags of the Army of Tennessee he has therein all the details of the other flag taken at Resaca.