This is all I have from the compiled service records:

Kuykendall, Abraham: Enlisted 3 Mar 61 (should be 62) at Ft McCulloch by CPT Scanland for 3 yrs. A PVT in Co’A’/Scanland’s Sqd. Paid 30 Sep 62. 30 Jun 63 on detach. serv. in pursuit of stray horses.

Kuykendall, John: Enlisted 14 Apr 63 at Camp Boluxie by CPT Scanland for 3 yrs. A PVT in Co’A’/Scanland’s Sqd. [Note: CSR says paid 30 Sep 62, but his enlistment is Apr 63.] AWOL since 27 Jun 63.

I doubt this helps much, but it is all I have.