I can't speak for USAF but they're probably stricter than the RAF. I came over from NZ and joined the RAF a few years ago. This process was enabled because NZ is a member of the Commonwealth. Any citizen of the Commonwealth can join the RAF provided they meet certain British citizenship criteria. That means having a British born parent or having either an ancestral visa from a British born grandparent (which enables a 4 year working visa) or a Right to Abode, all of which are slightly different.
The UK Armed Forces will accept Commonwealth citizens during their first 5 years BUT be prepared for grief over security issues, especially if you are going aircrew as things like aircraft tactics manual are usually classified for UK Eyes Only. So you may end up getting through elementary flying training easy enough, only to find that on a flying squadron you can't get combat ready or you won't be privvy to certain briefs because you are from somewhere dodgy, like Australia.
No matter which way you end in up in the UK, if you stay legitimately for 5 years then you can apply for a British passport. If you're really keen then you can renounce your original citizenship and become proper British, old chap. The Brits are pretty good about this once you have a British passport, but be prepared to get the persona non grata treatment from the Spams on exercises or ops unless you are single-nationality. This is not a decision you should take lightly, especially if you want to return to your home country, but you may find it restricts your career potential if you don't.
I'm not sure of the recruitment situation with aircrew at the moment, but a lot of initial intake training has been reduced over the years in all branchs and trades. Of course if you fail flying training, you can always go FC
for the '3rd man in the cockpit' experience. (snigger)
Good luck.
Edit note: Just saw that you are from writing from Singapore so you can probably get in under the Commonwealth rules.