Lambert's book got this flag wrong as well. It is an example of what we call the Hardee/Cleburne flag Type 1 - issued in March 1864 to Cleburne's Division.
The flag definitely was not at Richmond, KY.
I would suspect that McNair's Brigade carried flags like that of the 30th Arkansas which was lost at Stones River. Hill's/Cleburne's Brigade had Hardee flags while Smith's/Vaughn's Brigade carried Polk pattern battle flags.
I cannot recall if McCray's Brigade was organic to McCown's Division offhand.