ffmpeg is a command line tool that can convert .flv videos to .mp4 (or another format).
ffmpeg -i video.flv -codec copy video.mp4
Ffmpeg is easy to script, but the number of command line options can be daunting.
handbrake is a GUI application that can also convert .flv to .mp4.
Handbrake is actually a wrapper around ffmpeg that offers sensible defaults but still allows you access to many options.
VLC is an app that can view .flv videos directly. The VLC Player is free to use.