Sorry, but don't really know a lot about audio/video sync.

You may try to ask the support staff of the converter you like the most. I doubt that you may get any decent support for a free program, but who knows.

I use AVS Video Converter and Replay Converter. Both can convert FLV files and both support teams always were ready to help.
As for other software vendors, I had lots of problems with some chinese ones. Duno whether it is a language barrier or something else.