If you want to review any carrier's livery visit www.airliners.net where there are plenty of contemporary photos of each carrier.

The flag is not a legal requirement on US aircraft (unlike Switzerland, for example, where it has to be on the tail), and the application can be inconsistent, but many do have it.

Regarding flag orientation, it has always been the convention that flags are represented as if they were flown from the front, streaming back, and thus on the right (starboard) side of the plane they can appear reversed, but it's just the same as would occur if you were looking at a real flag being flown on a ship.

I always thought the "upside down = distress" concept only applies to the British Union Flag (not Union Jack, please), where you have to be sufficiently knowledgeable to identify if it is upside-down, and thus it is a signal that "I have been taken hostage by foreigners" without the foreigners actually realising it !