From my memories of 18 years of service in the RAF, most of the chaplains were C of E. I would guess that this simply represented the largest "congregation".
However, I do remember meeting the senior C of S chaplain who appeared on the flightdeck of my Belfast one day wearing a dog collar and also a set of RAF wings. When I suggested that he had therefore covered both qualifications for the entry into heaven, he told me that he had been a York captain during the Berlin Airlift before he had decided to log his flying time from the pulpit!
I also got to know an RC padre in Nicosia in 1964 or thereabouts. Unusually, he was a Benedictine monk who came from Ireland. He had a PPL and was also a qualified jumping bean (paratrooper). I think he also played rugby for Ireland at some point. Despite the fact that I came from the opposition (C of S), he and I became great friends and also got into a modicum of trouble from time to time.
As a result of one of our expeditions, he was sent to El Adem for 6 weeks as a penance by, as he described it, "I/C GOD; NEAF".
From which I deduced that "I/C GOD; NEAF" was RC and was also a Gp Capt.