This is a VERY common question for flute players and one I’ve been asked personally many times over the years. I used to think flautist was correct (or at least sounded hipper), but actually, flutist makes more sense. Why? Because flautist probably comes from the Italian “flautista” and since my language is English (American to be precise…), it’s flutist.
“Are you a flutist or flautist?”