A little info for Capt. Grace's Company can be found online at this link. Look under 1st. Regiment.
http://mississippiscv.org/MS_Units/MS_ST_Troops_Inf.htm

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:
http://mscgr.homestead.com/MSCGRSmithH.html