Hi again, I searched BLS GLO records, just for fun and found a Richard Burch owning 120 acres of land in Mississippi dated 1859 and specifically noted to be serving or noted as having served as a Private in Captain Beckham's Company, Louisiana Militia War 1812.

Legal land description being:

E½SE 11/ 16-N 1-W No Choctaw MS Holmes
SWSE 11/ 16-N 1-W No Choctaw MS Holmes

It was also interesting to note that on the land patent, the US Flag was waving backwards.

More info:
BURCH, RICHARD MS Holmes 1/21/1859 Jackson Doc.
Nr. 60913 Accession/
Serial Nr. MW-0264-002