You can use Flash CS3 Video Encoder (ships with Flash CS3) or if you using CS4 then you also get Adobe Media Encoder CS4.
Other then that, you can always open it in any adobe video editing software to convert.
There are aswell some other freetools around the net, search in www.videohelp.com for guides and such.
It appears that you can convert a .mpg to .flv with Adobe Media Encoder, but the audio disappears. Any way to make that happen?
Use MPG Streamclip to get the Mpg into a format you can work with..
It wont drop the audio..the prob there is that its muxed...this app is handy
I always use a free web-based app called Acethinker video converter to convert MPG video to FLV video, works pretty well for me. If you are interested in it, here are the steps to use acethinker.
Step 1. Run your web browser and visit the video converter, you can google search for it, this app compatibles with IE, Firefox, Chrome, Safari, Opera, etc.
Step 2. Click 'Select files to start' to open the converter and import your MPG videos.
Step 3. In the format drop down menu, select FLV as output format
Step 4. Click 'Convert' and select a folder in your computer to save the converted video.
Step 5. Click 'Start' to run the conversion, it will take a few minutes to finish the task, Once the conversion is finished, you can click 'Open folder' to located your converted video.
Try ffmpeg, just to change the container:
ffmpeg -i infile.mpg -c copy -f flv outfile.flv