For the noun denoting a person who plays the flute, Americans usually use flutist. In varieties of English from outside North America, flautist is more common. The web-searchable Canadian-English sample size is too small to be useful, but both words are used to some degree by Canadian writers.
Flutist, from the French flûtiste, is by far the older word in English, and it is not American in origin. The OED lists an example from 1603, though the word remained rare in any form until the early 18th century. It was the preferred form in all varieties of English until the late 19th century, when flautist, which came to English from the Italian flautista early that century, was fully adopted in British English.
If you can’t decide which form to use, flute-player is a noncontroversial alternative.
LeBaron’s “Solar Music,” which featured flutist Larry Kaplan and harpist Alison Bjorkedal, is full of striking, emphatic tonal colors. [Los Angeles Times]
But the principal flutist of theChicago Symphony Orchestra had some less than complimentary things to say about the Los Angeles Philharmonic. [New York Times]
A solo flautist played as the delegation returned to their seats in the Ancient Stadium. [London Evening Standard]
He was the product of that constantly imagining mind of Ian Anderson, singer-songwriter, flautist and guitarist of Jethro Tull. [Sydney Morning Herald]
They also had flautist and harmonica player Abbey Cindi, while Bahula was on traditional African drums. [Independent (South Africa)]