Richard,
That company does NO historical research whatsoever!!!!! Avoid using their flag images as they are not authentic.
I saw them at the Nashville CW show some years ago and challenged them on a number of flag images and they could not give me any concrete information on any of them!
In checking my files, the battery flag (probably A battery flag) was in the hands of some descendents of the unit as late as 1920. The Lyon County Historical Society has a reunion banner that is a Southern Cross pattern. Since they were part of the Army of Central Kentucky very early on, they should have been issued one of the Buckner/Hardee flags but without battle honors. I would have to dig into where they fought to see what other flags they might have carried.
Greg Biggs