One of the transactions listed on his Baseball-Reference page has him going from the Athletics to the Indians in a sale in October of 1955 "approximately."
Gray's register record has him going from the Athletics' system to independent San Diego before going to the Indians system for 1956. I could not find that deal, but I did find this transaction sending Gray to Indianapolis (in Cleveland's system) for the first time...from the Indianapolis Star of Apr. 28, 1956 in a season preview article about the Indy team:
“He'll have Ed Casque and Dolan Nichols ready and probably will try out Johnny Gray, new right hander purchased outright yesterday by Indianapolis from the Kansas City Athletics.”
So Indianapolis owned the rights to Gray, and they purchased him from the Athletics on April 27, 1956. Later, the Indians get Gray's rights in a complicated deal spelled out by the Lodi News-Sentinel of Oct, 17, 1956:
“The Cleveland Indians today acquired two pitchers and an outfielder from their Indianapolis and San Diego farm clubs in exchange for infielder Stan Pawloski and catcher Allen Jones, plus a small amount of cash.”
“...coming to the Tribe on the deal were pitcher John Gray of Indianapolis and pitcher Dick Mesa and outfielder Bob Usher from San Diego. Pawloski and Jones will go to the Padres.”
We can extrapolate from that that Cleveland bought the rights to Gray in a cash deal with Indianapolis on Oct. 17, 1956.
After spending the 1958 season with Philadelphia and their Miami AAA team, Gray heads to the Dodger group in an unexplained trade. I found this in the Schenectady Gazette of May 4, 1959:
"The Montreal Royals of the International Baseball league today bought right-handed pitcher John Gray from Philadelphia Phillies.”
Gray spent the 1959 season with Montreal and Spokane for the Dodgers, but was evidently sold to Vancouver after the season...from the Spokane Daily Chronicle of Oct. 16, 1959:
“…others cut loose were Spokane pitcher John Gray, who goes to Vancouver, B.C.”
Gray didn't play for Vancouver in 1960: his last year of playing ball was spent between three teams in two organizations...and I couldn't find the transactions for those.