The actual use of Texas state cflags as unit clors is not nearly as widespread as you might think. For example, so many people had come to Texas as immigrants after the Texas Republic of 1839, that when secession loomed in late 1860/early 1861, the Texas newspapers had to print descriptions of the 1839 Republic of Texas flag so that folks would know what it looked like. This was because after 1845 when Texas joined the USA, the republic flag was pretty much retired.
There is not much data on the flags of Sibley's Brigade in the New Mexico campaign but of the notices that I can recall the flags were all First Nationals. This dovetails pretty well with CS cavalry units operating in the Western Theater and Trans-Miss Theater in general - the First National flags remained in use with them well into the war and in some cases through the whole war. Unlike the cavalry command of the ANV Western cavalry did not seem to get standardzied battle flags of one pattern or another - with a few exceptions that we have noted.
We have never seen a cavalry unit with the design of teh flag of Walker's Texas Division (blue flag with red saltire/Southern Cross) but we have one cavalry unit at least with a blue flag and red St. George's cross from the Trans-Miss Theater - a variant of the Walker Division Flag.