The 13th USCT flag taken at Overton Hill was not a regimental banner - it was their National colors (Stars and Stipes). The inscriptions were painted on the stripes of the flag and that was a very common event actually.
The regimental flag (blue with US Coat of Arms probably) survived the war and was sent, along with loads of other USCT and other Union flags, to West Point. In the 1940's, those flags were destroyed as they were literally falling apart and nothing could be done then, it was felt, to conserve them. There were hundreds of flags involved.
The regimental flag of the 13th USCT is on the list of flags at West Point as #52 (the catalog number is very faint and I cannot read it off the list I have).
Secondly, I would love to see the account that the 19th Louisiana took this flag as every account I have seen states it was an Alabama regiment that did so and that the flag was sent to Alabama during the war (who knows where it is today). It seems to be pretty hard to see how a Louisiana unit would have sent the flag to Alabama! Pretty much all of the maps in books about this battle show the 13th USCT striking the right side of Holtzclaw's Alabama Brigade. Wiley Sword's book on this battle has an Alabama officer picking up the flag.
Please state the Louisiana account and cite the source please (book, page, etc.)