I doubt he is buried at Mills Springs as the regiment was not present. Someone with a much better understanding of Confederate movements at the time may be able to shed more light. If the date of death is correct, I suggest you look closer to Bowling Green with a possibility of him being one of the unknowns buried in Fairview Cemetery. Fairview Cemetery has another soldier by the name of "G.W. Kirksey, 1st Ark Bat" who died December 5, 1861.