I believe it’s the same in German. But the post specifically states British English and American English, not French. Just sayin.
Also you bring up a new point that has always confused me. Flights of stairs. What is that? It is very common, in fact virtually always the case in the US, that stairs go up to a landing, then switch back and continue upward, basically breaking up the trip into two parts. I’ve never known if a “flight” is one of those two pieces or the whole trip. Something tells me it’s both.
British English might have continental Europe influences there whereas American English doesn’t? Dunno, don’t have an explanation for the difference.
As for the “flight”, I’ve always wondered that myself, but never bothered to googled it. Simply assumed it was used for both. Just googled it now, and the consensus seems to be that a flight is an uninterrupted row of stairs. So if you have one of those spiraling staircases and it doesn’t stop for 200 steps, that’s one flight of stairs. If you have those zig zagging steps that you usually find in modern buildings, even tho there’s only one floor between them, if there’s a platform in between, that’s 2 flight of stairs. So… There you go.