"Slightly "Air America" without the CIA bit perhaps?"
Most of the FT work was pretty kosher. It was the unit which the AVG boss Claire Chennault formed after WW2 which is perhaps what you are thinking of. Called Civil Air Transport, or CAT for short - it was formed in 1947 using ex USAAF C46 Curtis Commandos with UN cash. It was formed primarily to fly relief around China and get the local economy started. However, it had to be bankrolled by Chinese businessmen and during the Communist uprising, eventually became part of the Nationalist forces air wing. Eventually, it ended up in Taiwan with no routes left when the Korean war started.
Then the US governemnt got interested in them and awarded them lots of contracts in Korea, then in South east Asia (Vietnam) doing all sorts of clandestine stuff such as dropping spies in the Peoples republic of China to flying French Airforce C119s into the battle of Bien Dien Phu. It's pilots could be dropping paratroopers one day, flying first class passengers the next. They finally folded in the 60s, but elements became Air America and several other assets got passed onto other airlines. For example, China Airlines now owns Mandarin airlines and still uses the CAT callsign "Mandarin" for some of it's flights.
An interesting history of the most shot at airline in history can be read in Felix Smith's book, 'China Pilot' available on Amazon. It's a great read by an unusual animal - a pilot who can write well!