Roster of Confederate Soldiers, 1861-1865 does not show a Samuel K. Oates, Jr but does show the following:
Oates, George KY Cav. 2nd Bn. (Dortch's) Co.C
Oates, George KY Morgan's Men Co.G
[which could be the same man listed twice]
Oates, James M. KY 10th (Johnson's) Cav. New. Co.I
Oates, W.A. KY 10th (Johnson's) Cav. New Co.I