I have done it using Jack audio server   :
- Install jackd and qjackctl : say "yes" when asked to have real time access right, then reboot to apply this access right.
 
- Stop temporarily pulseaudio with this 3 commands :
mkdir ~/.pulse
echo autospawn=no > ~/.pulse/client.conf
pulseaudio -k 
(Later, to revert to pulseaudio normal mode, run echo autospawn=yes > ~/.pulse/client.conf then pulseaudio )
- create .asoundrc  (the point is important) in your home dir containing :
 
pcm.!default { 
        type plug   slave { pcm "jack" } 
    }
<p>pcm.jack {   type jack<br>
playback_ports {
      0 system:playback_1
      1 system:playback_2   }<br>
capture_ports {
      0 alsa_pcm:capture_1
      1 alsa_pcm:capture_2   }   }</p>
<p>ctl.mixer0 {   type hw   card 1 }</p>
Run qjackctl from sound menu, click "start", click  "connect" to display "connections" windows.
 
Launch 2 differents SimpleScreenRecorder , chose "jack" as audio , start preview mode to display vumeter in both
 
- Launch Firefox and Chrome, play video in each
 
- Go to qjackctl   "connections" windows , drag and drop   from  the first left side "jack-alsa-xxx" to  the first right side  "simplescreenrecorder": you will get a connection displayed and vumeter will move in the first simplescreenrecorder. 
Do the same for the second "jack-alsa" and "simplescreenrecorder"
 
- Now you can record  audio from each browser in each simplescreenrecorder 
 
May be Firefox has problem with html5 and jack audio server in youtube,  I have only tested with flashplayer.
