Hope This helps
It is not necessary for a Royal Marine to assume another rank/service just because he goes fast jet with either the RN or RAF. At some stage he might elect to transfer between services (David Morgan DSC post-Falklands: RAF 2 RN) but that's a separate issue.
There are opportunities for officers to 'exchange' between services in many specialities, not just FJ or even flying.
Jock Stirrup wears the 'RAF Flying Badge' because he is a qualified pilot. There is no 'fast jet' badge per se. One is entitled to wear flying badges awarded, even if not actually employed on flying duties, unless there is some reason to rescind the award eg does not complete all training for the retention of the badge.
When one stops active flying, one can elect to wear any of the aircrew badges for which one qualified (used to work with an RAF officer who wore the Glider Pilot badge awarded when the RAF sent him to fly Horsas across the Rhine in 1945 - looks v smart on a No: 1 as well).
As for flying fast jets, the services don't have an age limit (it used to be 47 for flying pay at one stage) but it depends on need, proficiency, medical fitness and a host of other criteria. The Jaguar force deployed a 54(?) year old FJ pilot to Gulf War One but in general terms there is a natural scaling back as the years' progress and relatively few pilots or navs are still on fast jets at chucking out time (generally 55) {there will now follow a series of posts about somebody's dad who was still at it at 97}
Hope this helps.
O-D