We call these Bragg pattern battle flags, second issue. The AOT flags were those issued in 1864 from the Augusta Depot.
Regarding the naval jack sold by Heritage, who knows other than it was the jack for whatever vessel that Parker was with during the war. The surviving members of the James River Squadron were indeed mustered into infantry units in 1865 and some did have battle flags. The crew of the CSS Nansemond did, a late issued ANV flag from the Richmond Depot, now in private hands.
How sure are you that Parker was with the CSS Patrick Henry? Can you cite something for that please?
Greg Biggs