Never heard "flutter" in connection with a bet until I went to the horse races in Ireland. Immediately knew it was a small bet ... context I guess.
I think US became acquainted with the term when all the BBC stuff crossed the pond .
There was a PBS (Public Broadcasting System) program about Britain's Royal Family which had a bit showing Her Majesty at the races and she was heard to make a 10-pound bet. Guess that's a "flutter" to her!
A flutter in US would be a $2 bet! Or $6 if you were betting "across the board" which would pay out if your horse won, placed (2nd) or showed (3rd).

"Tipple" would give you away as British in most US bars