The regiment was officially mustered as the 13th Tennessee Cavalry as there was already an 8th Tennessee Cavalry regiment in existence earlier (Baxter Smith's).
I am doing the book of Tennessee Civil War flags and no flag has been located for this regiment although one was displayed in Nashville in 1897 during a special exposition in the city. In early 1864 they did receive as part of Joe Wheeler's Cavalry Corps a new Augusta Depot made flag. These were rectangular with 13 stars and no colored border. The flag for the 6th Tennessee Cavalry of this issue exists in the collections of the Tennessee State Museum in Nashville. It is unmarked with any unit designation.
Sorry not to have more information for you.
Greg Biggs