I play the flute or, as I usually say: I am a flutist.
When I tell this to people, they frequently interject, “Oh, is that how you say it? Not flautist?” Both words are correct, however “flutist” feels more comfortable to me than “flautist.” I have even heard British friends say “flawtist.” Although it’s purely my personal preference, apparently the word “flutist” predates “flautist” — which is derived from the Italian word “flautista.” Many years ago, when I first met the famous flute player James Galway, those were almost the first words out of his mouth to me: “Don’t ask me if I’m a flutist or a flautist. I play the flute — I am a FLUTIST.” And that’s a good enough reason for me!