There were several units stationed at Ft. Brown. The US First Infantry, Seventh Infantry, Second Artillery and Third Artillery were there prior March 1861. The Fort was then occupied by Texas State Troops for a while and by August 1861 the Second Texas Rifles (CSA) were stationed there until the middle of 1865. The Second Rifles were also known as the Second Texas Cav. It would appear that maybe the Texas State Troops were presented the flag you mention.