Depends how far you want to go back, the USAF
dates from 1946? Before it was part of the Army, then you have the Navy and Marines.
The RAF was formed in April 1918, before it was the Royal Flying Corps, then there was the Royal Naval Air Service, but they were under RAF control (and suffered neglect) between I think 1918-37.
The disadvantage the UK services have is that between Suez in 1956 and the Falklands, despite being 'busy' for virtually all of the time, they did no air to air until the 1982 war, and have not since.