Hopefully this summer I will, begin working on the book of Tennessee flags for the state museum. I have large files for the flags of TN units.
No flag survives for the 19th Tennessee (Biffle's) that we have been able to locate, and other than the flag for the 9th TN Battalion being in Texas as of the early 20th Century, that's all we know about it. Perhaps the Maury County newspaper ran articles on these reunions that may have mentioned the flag, or after they could print photographs, an actual picture of the flag.
Please also know that you are probably talking of more than one flag for each of these units. I know of no CS unit that carried the same banner through the entire war from 1861-1865. Battle damage, transfers and pattern changes usually brought new flags. Western CS cavalry did not follow the lead of the various infantry corps of the Western Theater by going with standardized patterns until late 1863 although there were some attempts with the Bragg pattern flag of March-Summer, 1862 based on a surviving flag for the 1st Alabama Cavalry.
Looking over the service record of the 9th TN Cavalry Battalion I can surmise they had at least two flags during the war: at Donelson it was a First National, which was the dominant pattern of flag from 1861-1863 for Western Theater cavalry units.
In November, 1863, they were part of William "Red" Jackson's Cavalry Division and, since that division received the first of the rectangular 12 star saltire battle flags from the Mobile Depot, they should have gotten one of those. This flag is commonly (and incorrectly although his corps would get them in July, 1864) called "Forrest's Battle Flag." In actuality it would serve units from the Dept. of Alabama, Mississippi and East Louisiana including Polk's Army of Mississippi, the Mobile Garrison, Roddey's Division and Forrest's Cavalry Corps.
If they, for some reason, did not receive this flag in November, 1863, then, when they became part of Wheeler's Cavalry Corps for the Atlanta Campaign of 1864 in March, they may well have been issued one of the Augusta Depot rectangular battle flags with 13 stars, as part of the general new flag issue to the Army of Tennessee.
So we are looking at least at two flags for the 9th TN Cavalry Battalion.
As for Biffle's 19th Tennessee Cavalry we are also looking for at least two flags - their First National under which they would serve from 1861-1863 most likely and then the Augusta Depot flag of early 1864 when they were part of the general issue of new flags to Wheeler's Cavalry Corps for the Atlanta Campaign..
The big "what if" for both units is if they also received replacement First Nationals at any time during 1862-1863 that we do not have a record for.
Hope this was of some help to you.