Cavalry flags.

In Column South (1953), set at Fort Union, New Mexico, in January 1861, dialog indicates the command consists of two troops or companies, A and B. The cavalry at fort Union have two guidons, or company flags, that are fork tailed and red above and white below.

From 1833 to 1862, such guidons had "U.S." in white above and the company letter in red below. From 1885 to the present red and white cavalry guidons have the regimental number in white above and the company letter in red below.

in one scene it is easy to see that one of the red and white guidons is marked "2" above and "A" below, standing for Company A of the 2nd US Cavalry Regiment. This shows that parts of the 2nd US Cavalry are stationed at Fort Union in 1861 in the fictional universe of the movie.

In real history, the Second United States Dragoons was stationed in Utah and Texas in in early 1861. It was renamed the Second US Cavalry Regiment in August 1861. In early 1861 the Second United States Cavalry Regiment was also stationed in Texas and other parts of the Southwest. It was renamed the Fifth United States Cavalry Regiment in August 1861.

Another flag seen in the movie may represent artillery stationed at Fort Union. It is red, fork-tailed, and has a yellow "8" or "B" above and yellow crossed objects - I couldn't see if they were sabers for cavalry, or rifles for infantry, or cannon for artillery. Present day field artillery guidons are scarlet red, and fork-tailed, with the regimental number above, the company letter below, and crossed cannon barrels, all in gold.

Thus the design of that red guidon could have been based on field artillery guidons.

https://en.wikipedia.org/wiki/Guidon_(United_States)

And also see this post: https://moviechat.org/tt0036677/Buffalo-Bill/5b59505a2433d9001410270b/Cavalry-standards-and-guidons/edit where a somewhat similar guidon in Buffalo Bill (1945) is mentioned. I suppose it is possible that the same prop was used in both movies.