Parachute Regiment Battalions didn't have a flight!
No they had a Squadron, 664 Parachute Sqn AAC. Disbanded 1976/77 when 16 Parachute Bde was disbanded. I would suggest the aircraft with Pegasus on the door was a 664 Sqn cab and certainly 1 Para did a Cyprus UN tour, maybe more, almost certainly a flight from 664 would have accompanied them.