I know that a piece of software called "KRAD
RADIO" can do this kind of
 stuff. Though it's still in a stage of development where things change
 often and redically, version tagged as "13" in github is quite stable:
 
https://github.com/krad-radio/krad_radio/archive/Version_13.tar.gz
 
I had problems with compiling that tarball.
./waf configured barfed:
So I used git tags:
  After you build from source, you basically fire up a
"station", set the
 (output) resolution and framerate, add the X11 capture for the live
 image, add a jack input for the audio and set up the
 "record-to-file"-part, specifying the codecs (WebM by default).
 All commands needed are documented here:
 
https://wiki.mozilla.org/Krad_Radio/Commands
 and some example "sessions" can be found here:
 
https://wiki.mozilla.org/Krad_Radio/Snippets
 Live streaming the output is also possible.
 If you have any questions, you can visit the devs in IRC at
 
irc://orc.mozilla.org/#kradradio  or ask me:)
 Best regards,
        Jannis