You have a couple patterns that were not at Franklin at all and within one of those listed not specific enough as to type.
Army of Tennessee pattern (Southern Cross, Augusta Depot - the predominant flag pattern at Franklin); Army of Mississippi/Dept. of Alabama, Mississippi & East. Louisiana pattern (12 star Southern Cross from Mobile Depot); Charleston Depot (at least Gist's Brigade and maybe a few more - Southern Cross, square pattern but not the ANV Richmond Depot flag); Hardee 1864 pattern (Spring and Fall issues - Cleburne's Division); possibly a Bragg pattern (12 star Southern Cross, H. Cassidy made - Lumsden's ALA Battery); First National (a couple artillery batteries had them - one has a Southern Cross canton - one taken at Franklin and one at Nashville) - and that pretty much covers it. Oh yeah - the Texas regiments of Ector's Brigade had ANV Fourth Bunting battle flags from the Richmond Depot while the two NC regiments fo the brigade had Mobile Depot flags.
There were no Van Dorn, Bowen/Price or Polk pattern flags at Franklin that I am aware of. By March 1864, the Army of Tennessee had pretty much standardized their flag patterns so these other flags used by the army were pretty much replaced by then.