Public parks are the perfect setting for an impromptu music session -- this is usually an informal, relaxed atmosphere where you can play and have fun, without the pressure of an audience focused exclusively on you. Playing in parks is a good way to get comfortable with playing in public places without playing for anyone in particular, except yourself.
Find a pedestrian-only street in your town or city. Depending on the amount of exposure you want, choose a busy part of the street to receive more attention, or a less crowded spot if you just want to contribute to the atmosphere. This is also a good way to practice performing in public without being in a concert setting. Make sure to check ahead if your town or city requires a license to perform on the street.
Get to the roots of the instrument by playing in nature, away from the noise of a city. This will allow you to play in a tranquil setting and focus exclusively on the music you are playing, without any human disturbances. If you are not comfortable playing in front of people yet, playing in nature is a good way to practice your flute.
You can play your flute solo or with other players for friends at a house or apartment. This creates a more intimate environment, where your audience focuses on you and the music. This can be a good way to build a fan base if you are trying to begin performing. Make sure to practice beforehand and to get your accompanying musicians familiar with what you will be playing.