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There are two common types of files that carry the .fla extension. Firstly you might have a Macromedia Flash Authoring file. This can be opened with Macromedia Flash software for editing.
Another type of file you might have when you get a .fla file, is a FLAC music file. FLAC stands for Free Lossless Audio Codec. It is open source and provides lossless audio compression. This means that even though the audio is compressed, it will still maintain its exact original quality. However, since it is lossless, music stored in this format would definitely take up more space than say MP3 or Musepack audio or any other lossy compression.
Foobar 2000 is an excellent audio player that can play back the FLAC audio format. If you wish to burn music from the FLAC audio format to an audio CD, you can get a plugin for Nero Burning Rom here.
Related software tools
Foobar 2000 (Freeware)
Foobar is an advanced audio player for audiophiles
Nero Multimedia Suite (Nero Burning ROM) (Shareware)
Nero is the best and most complete DVDR / CDR / Blu-ray all-in-one software