For the first step, the Riva FLV Encoder is a convenient (Windows only) free tool for transcoding existing AVI, MPEG, MOV or WMV files into FLV. (Note: this is basically a GUI wrapper for ffmpeg.)

On Linux (or on Windows from the command line), you can use ffmpeg or MEncoder (which includes ffmpeg).

For including the resulting FLV in a SWF for playback in the Flash player, see Klaus Rechert's excellent tutorial on adding streaming multimedia to SWFs. He also provides Ming patches to enable adding FLVs to SWFs.