>>>The 16th came to Chickamauga with others of Thomas Cobb's Irish Bridgade.>>>
So far as I know, Cobb's Brigade was mostly non-Irishmen. Of the units in the brigade, the one wrongly depicted as being Irish (and a unit flag made up to be so appeared in the "Gods & Generals" movie) was the 24th Georgia of which only one company was Irish (the McMillan Guards). Most of the unit was not Irish.
I am writing a book on Georgia Civil War flags and no "Irish" flag for the 24th Georgia or the brigade exists.