Wayne & Jim,
The flag fragment at Nicholls State U. is very small
perhaps 1" square. It suposedly is part of Company
K's flag.
The flag lost at Rappanhannock Station was indeed
replaced on Feb. 1, 1864. See Compiled Service Record of Lieut. John S. Dea, acting Adjutant.
I have seen no documentation that indicates the Regiment either surrendered a flag or cut one up to prevent capture at Appomattox.
Either scenario is possible.

Ken Legendre