The question is incorrect.
FLV is not a compression, but only the container format of media files (Flash Video), which can contain audio/video streams with different compression.
If on fingers: the Media file is a collection of compressed streams (audio, video, tekstowych) Packed in a special way in a certain container format. Total for media playback you need:
1. A demultiplexer (demuxer) [in the form of splitter or parser] — to retrieve a specific container format (e.g. AVI, ASF, MKV, OGM, MPEG-PS, MP4, MOV, FLV) directly themselves naked but at the same time compressed media streams.
2. The decoder for the video stream, for decoding the extracted compressed video stream (e.g., decoder for MPEG-4 ASP, MPEG-4 AVC (H. 264), Theora, VP8, etc.)
3. The decoder for the audio stream for decoding the extracted compressed audio stream (e.g., decoder MPEG Layer-3, AAC, AC3, Vorbis, FLAC etc.)
But the issue appears only container format of the media file (which can only be called the right demuxer) and no indication of compression of the audio stream and video stream, so it is impossible to offer the necessary decoders for them.
In the container are Packed FLV video: FLV1 (Sorenson Spark), VP6, H. 264 and audio: MPEG Layer-3 or HE-AAC.
Depending on the particular compression stream and need to select the appropriate decoder.
If you play under Windows using DirectShow-based media players, then a good option is to use DirectShow to decode audio/video and any FLV DirectShow Splitter to demultiplex.
However, I am under Windows and under Linux for demeksa and decode prefer to use ffmpeg libraries (libavformat, libavcodec), which is used in mplayer, VLC media player etc. opensorce projects.