I've tried using your app in Chromium (on Ubuntu 12.10), but the the flash permission doesn't show up (http://imgur.com/VD25h). It seems to be working in Google Chrome, though.
It's been a rough ride for us regarding browser compatibility. In the beginning we wanted to support them all, but then quickly boiled it down to just Chrome. It's a really good browser for prototyping. At first we wanted to use native controls for audio recording, but quickly realized that it won't go, because it's still very beta. We decided to use Flash for voice recording, but a week ago Google surprised us with a broken release. We're sure they'll fix it soon. In the future we'll be more careful and will consider Firefox and others also.
Sad thing one that google part, but I hope you'll be able to move away from flash soon.