A flautist is a person who plays the flute. This spelling is the usual one in British English. In American English you will more often see flutist, built straight from flute; both words name the same job. A flautist may be a child in the school band or a player on a concert stage. The word can sound a little more “classical concert” than flute player, but it is not showing off; it is just the name of the player. Though actually, in jazz and pop people often just say flute player.