Hi,
yes, this is quite a commom problem, and there are two solutions : one is called pulseaudio (
archwiki).
The second is dmix (
archwiki), which I prefer, but is a little more complex to setup. Also dmix should be enabled by default on 2.0 stereo outputs.
Just out of curiosity : does using two applications which are not flash (or skype or anything proprietary) at the same time work?
Serafean