The 5th/13th Arkansas has not been seen by me but it has by peop,e who I know who know flags. I have a drawing of it.
As for the 3rd Arkansas Cavalry, they did get a Van Dorn flag in September, 1862 as part of the Army of the West and may well have been carrying it at Thompsopn's Station - but we just do not know for sure.
Greg Biggs