A little info for Capt. Grace's Company can be found online at this link. Look under 1st. Regiment.
There are two men named Smith in the roster of this company.
Rank In / Out
J.K. Smith Corporal / Corporal
W.R. Smith Private / Private
I'm assuming this is your Jacob Kynerd Smith buried in the Boyd Cemetery in Neshoba County:
Smith, J. K. No dates, Paton's BN CSA
Smith, Jacob Kynerd Dec 27, 1847 - 1937
He is listed as Jack K. Smith at this site: