So many options... What to choose?

If your FLV files use h.264 video codec and you want to get MP4 files without transcoding videos, then just remux FLV video into MP4 using freeware software.

If you want to get MPEG-2 or WMV files fast, then you may try Replay Video Capture (or any other screen video capture software).
Please note that recording videos from screen is resource intensive especially when you re-record HD videos, so your computer should be powerful enough. But you can always record with Replay Media Catcher and then use video editors mentioned above.