Most of these barracks were purpose built for the military, and are very difficult to convert to other uses. These days it is far cheaper to pull something down and build new, rather than trying to convert.
As for transport, I remember going on Flying Falcon from 3 Div (Bulford) in combats, travelling in coaches and flying in Britannias from Brize to Gutersloh.
When we were deployed on Op Exit in Malta (1972) it was in civvies, in the back of an MK and flying in a Herc from Lynham.