Martha - Their records with 1st Tenn (Carter's) Cavalry, Co. C, do not record the death of any of these men. The first brother to enlist was JKP, Aug. 26, 1861, at Knoxville by D. M. Key. Another Davis, H.B. or Henry B. (possibly the uncle?) enlisted in the same company at the same time - rank 3rd Corporal. On the regimental return for June 1862, both of these men are shown "Detailed as escort by order of Gen. Stevenson since 20 June ". H.B. was reduced to private on Jan. 15, 1863. As you noted, JKP is shown as "Missing since Battle of Bakers Creek May 16/63." Note: Company C, at this time, was serving on detached duty in the 4th Brigade of Gen. Stevenson's Division under Col. A.W. Reynolds, and thus would have been present at Baker's Creek.
William enlisted Nov. 14, 1861, at Cleveland by Gen. Gillespie, and Benjamin on Jan. 24, 1863, at Vicksburg by Captain Van Dyke. From there the records of H.B., William, and Benjamin are almost identical. They were captured (surrendered) at Vicksburg. July 4, 1863, paroled on July 15, 1863, and appeared on a list of sick and wounded prisoners shipped on July 24, 1863, from Vicksburg to Mobile via New Orleans. Only Benjamin appears again, signing a receipt for clothing on Sept. 30, 1864.