If frames are missing, I'd think that the web flash player would have the same issue.
Most media players that work with the flv container simply parse the codecs directly. However, Sothink Flv Player uses the adobe flash decoder, so it plays flv files much like a web flash player would.
Also, most video converters parse the codecs directly, but
Moyea Flv to Video Converter Pro 2 also uses an adobe decoder, and parses all of the flv container timestamps. This is why the moyea converter will often work well with livestream flv files that may have non-linear irregularities.
But if frames are missing, nothing is going to create them for you. If the content was one-of-a-kind, it might be worth the trouble to edit the flv timestamps for the duplicate frames to match the previous frame, so the audio would not advance - and then run it through the moyea converter. But this still would be a lot of work.
Does the HQ version have the same problem? Maybe they will eventually post 1080p versions. As far as the current HD version, it is just hard to take bad input (with missing information) and make it good.