Dont forget their Uniforms.
I never learned them in the first place so I can't possibly forget them!
On a more serious note,
@rob2001,
@Virginia Liberal &
@BarrelBuster, please consider me well and truly handed my marching orders; I'm not good enough at the art of illustration to have a diagram worth posting, but I do have some notions; for the record, this description will only cover the Second Republic of Texas circa the end of 2GW (with perhaps a few allusions to the postwar era).
In brief, one imagines that the State of Texas - being amongst the biggest & most populous of the Confederate States even after that disagreeable business with the State of Houston* - would have made a point of being as self-sufficient as possible in terms of war supplies (One imagines terrible wrangles during the First Great War and some truly delicate negotiations prior to the Second, given that in the aftermath of the Knight Coup Featherston has
excellent reason to mistrust Texans, while Texas has ample reason to believe that if they can't make it for themselves, they'll go short as the Confederate Government focuses east of the Mississippi - a situation likely to be further complicated by Texas being the natural focus for Confederate rearmament-on-the-quiet, given it's proximity to the Mexican 'proving grounds' and it's enormous spaces).
In other words the Army of Texas might well be one of the largest to be found in a secondary theatre and unusually well-equipped (though Featherston would probably keep the very best goodies under his own watchful eye back east), though I suspect there would be a very significant concentration of Freedom Party Guards in the Lone Star State to keep the Texas State Government honest - something that might well have contributed to Texas' willingness to go it's own way once 'Sarge' started losing his grip on the South.
*
I'll bet you cash money that Texans don't use that name if they can possibly avoid it, preferring various circumlocutions or simply "That place" (or perhaps "Our old place").
With that in mind I tend to assume that the Army of Texas (probably majority-Texan, but with odds & ends from other states complicating things politically) would wear fairly conventional CS Army/Air Force uniform of the Second Great War - albeit with sensible adaptations to better suit the frequently broiling, sun-baked Lone Star State (Cowboy hats in place of kepis, for instance, and white dress uniforms** for example); this would, of course, leave troops willing to work with the United States in a somewhat awkward position once the Second Republic is proclaimed, since all those other fellows NOT willing to do business with the 'DamnYankees' will likely be wearing the exact same outfit (an outfit the US army et al have been shooting on sight for several years).
Assuming that the US Army does not go out of it's way to be helpful in terms of resupply - which I think we can most reasonably assume to be the case - the newly minted Army of the Republic is likely to emphasise field modifications like removing stars from the rank badges of field officers (in the interests of leaving only a Lone Star), adding a star to the badges of lower ranks for the purposes of differentiation, painting a Lone Star on helmets or wearing a simple 'white above, red below' armband (a nod to the field of the Texas state flag).
I'd also be very surprised if there weren't a thriving black market in US army 'Coal scuttle' helmets destined to be repainted butternut and prized as the best way to avoid triggering a US soldier's instinctive fight-or-flight response; one assumes that weapons & equipment would remain much the same (though with 'CSA' stamps*** or logos either defaced, removed or just turned upside down as shorthand for a soldier's change of allegiance).
**
I'd bet money that it isn't just the CS Navy that has dress white uniforms, given the generally steamy, baking-and-or-boiling local climate.
***
I've imagined a 'CSA' army stamp with the letter 'C' resting above the 'SA' to form a sort of pyramid (Suggesting a 'Confederacy and the rest' mindset), but am not sure how practical this might be.
It's also quite possible that those Republic of Texas officers working in close proximity to the US Army for prolonged periods might well take to wearing US insignia on (ex)Confederate Army uniforms - I'm specifically thinking of staff officers in the field grades, major & lieutenant colonel & full colonel - to help avoid confusion with the insignia of US Army brigadier generals, major generals or lieutenant generals AND make life harder for infiltrators who might assume that their old dress uniforms will help them slide in & out unnoticed.
Meanwhile, I'm fairly confident that any Featherstone-Aligned former comrades in arms will become even more ragged as their lines of supply are cut off; with that in mind, I'm not sure they'd be able to make even field modifications to their uniforms, but die hards are likely to gravitate to Freedom Party Guard formations (suggesting either the placement of Party Guard insignia on CS Army uniforms or - more likely - a strange mix of Party Guard, CS Army and scavenged US Army kit).