Wasn't the Van Dorn pattern flag for the 17th Arkansas Infantry taken at Port Hudson?
The large First National garrison flag taken there survives and is back at the park itself.
The CS flags at Port Hudson might be along the lines of the CS flags taken at Vicksburg; none were sent to the US War Department (some 80 flags taken at Vicksburg). Some were given to officers (Gen. Frank Blair loaned two to the Cincinnati Sanitary Fair in December 1863) and who knows what happened to the rest.
I don't think I have seen how many flags were taken at Port Hudson before.