As far as currently known Jimi played with Percy Sledge only on one occasion, the release party of the Percy Sledge lp "When A Man Loves A Woman". This occasion is quite well documented mainly thanks to the wonderful photographs taken by "Popsie" (note the lp sleeves in the background) : http://www.popsiephotos.com
Be sure to check the entries for the other artists present at the party since the Jimi Hendrix & Percy Sledge -pages don't contain all of the photos available.
Jimi appeared as a member of Curtis King & the Kingpins who seem to have acted as the house band at the party. They can be seen backing Percy Sledge performing solo and singing a together with Esther Phillips and Wilson Pickett. They also backed a "solo" Wilson Pickett and possibly played a solo set themselves (one of the photographs shows the band playing in the background with Percy Sledge, Esther Phillips and assorted other people posing for a "press photo" in front, no vocalist singing is visible). The Popsie website dates the photos as being from 5 May 1966, no location is given.
Additionally, the liner notes of the 2nd Percy Sledge lp on Atlantic ("Warm And Tender Soul" Atlantic SD 8132 released in 1966) have this to say: "Percy Sledge comes from a small Alabama town called Leighton. His first trip to the Big City came shortly after his first hit. We met him when Atlantic Records threw a "welcome" bash at the famed Prelude Supper Club on New York's upper Broadway. Percy was as dazzled by the bright lights as the critics and radio people were dazzled by his performance. As part of the "fun-and-games" that night, he and Esther Phillips sand a duet version of When A Man Loves A Woman while King Curtis and his band backed them up. Percy and Esther sang nineteen choruses of the song before they finally quit " The liner notes were written by Jack Walker of WLIB, New York who must have attended the party one assumes.
The mention of "critics and radio people" is intriguing, were there perhaps interviews or live recordings made or were the "radio people" there only as vip guests? The writer of the liner notes was probably a dj so that might be the only reason he singled out "radio people" but you never know...
A 3rd source of information is a post made by Cliff Malloy, historian for the Popsie estate, he states: "Also present that fateful night were Esther Phillips, Don Covay and the one and only Wilson "Wicked" Pickett." From this it is not quite clear wether Don Covay also performed at the party, so far no photos picturing Covay at the party have surfaced. He also gives the location as the Prelude Club.
So the location, date and line-up of the party would seem to have been as follows:
Prelude Club, New York City, New York
Thursday 5 May 1966
King Curtis & the Kingpins
Don Covay (?)