I don't think I can make any claims about continuity between the uniforms and equipage (what Brits call "kit") between the Lonestar Republic's armed forces--such as they were--and later Texas Confederates, but it is a fact that many ready-to-wear red flannel shirts, and others of linen "Russia duck" were purchased by Texas purchasing agents in New Orleans after San Jacinto... That, and an initial order of 500 leather caps, followed a bit later by fully 1,093 leather caps, which are commonly thought to have been the hideous and impractical Model 1833 leather forage cap that the U.S. army was using--however briefly--at the time. There is also evidence--much of it conjectural or speculative--that the Texas Republic army used red wool blankets. So while the fatigue uniforms were gray with black trim, or white, and the dress uniforms were dark blue and white for infantry, there was a "flash of red" here and there. The Texas army's NCOs tied their red sashes up on the right side instead of the left. When the Civil War began, there was considerable use in Texas of the materiel surrendered by David Emanuel Twiggs, which was supplying about 1/5th of the total U.S. army in distant frontier posts. Many Texas CSA uniforms were, wait for it, gray with black trim, albeit in a more modern cut. The State Penitentiary in Huntsville had looms and textile mills, which produced undyed woolens and jean cloth, which were the color of the sheep that produced it... Typically off white, white, or a very light gray. I know that the 6th TX infantry, CSA wore mostly butternut jean cloth uniforms when they were with the Army of the Tennessee.
I also might add, that in the various pre-modern and un-scientific thinking that was still very common in the 19th century, the color red as used in drawers like the so-called drop-seat "union suit" was thought to be healthier for the wearer. So if red long johns, presumably red shirts too?