Jellyfin should work fine for what you’re looking for. I haven’t run it on a Pi but it should work on that. You’ll be able to play music using the web ui as well as mobile apps if that’s your thing. It can also transcode on the fly so if your current browser/device/whatever can’t play .flac directly it’ll automatically transcode the playback to .mp3 or whatever it needs to be.
There are some other self hosted music/streaming projects you could take a look at that are much more built out for music playback specifically. Look into Airsonic-Advanced or Navidrome for example - I’ve been meaning to check them out myself but haven’t gotten around to it yet.