I have written an article on CS cavalry flags for the Western Theater and for the most part from 1861-1863 they used First National battle flags. There were some exceptions of course - some Polk Corps flags used (Dawson's TN partisan Rangers had one), a few Bragg pattern flags used (1st Alabama Cavalry had one - rectangular version) and even some Second Nationals (1864 in Forrest's Corps), but unlike Lee's army in Virginia, the western CS cavalry did not start to standardize their battle flags until the Fall of 1863 when the first Mobile Depot flags were issued to Jackson's Cavalry Division. As I have noted already, S. D. Lee's Cavalry Corps got them after that and then Forrest's corps in July 1864.
The cavalry of the Army of Tennessee got their rectangular, thirteen star Augusta Depot battle flags starting in February-March, 1864. When Polk's Army of Mississippi was added to the Army of Tennessee in May of that year, they brought their Mobile Depot flags with them including Jackson's division of cavalry. For the rest of the war in the west the cavalry's flags were pretty much standardized.