Sorry to hear that, I remember how annoying that is.
There were discussion threads up on the official ASUS forums concerning this issue a long time ago. Not sure if they're still going after all these years. Last I checked, there was no official word on how to fix it.
It's possible that this might not be a driver or even chip specific problem though and something else is at fault here (some mobo/soundcard incompatibility, software configuration). I've seen Auzentech, Creative as well as external DAC owners reporting the same or similar random noises coming out of their speakers/headphones. That and the fact that it's so rare is what made me stick with STX. Even if I did get another DAC and it actually wasn't the card's fault, it could take a few long months for the problem to rear its ugly head again.
As for Flash, if you're using YouTube, couldn't you switch to the html5 player? https://www.youtube.com/html5
EDIT: As I stated before, I don't have this problem anymore even though I'm still using the card and I haven't done any significant changes to my hardware or software setup.
Also, I posted these links earlier in this thread. They threads are long dead:
http://vip.asus.com/forum/view.aspx?SLanguage=en-us&id=20090222084608127&board_id=21&model=Xonar%20Essence%20STX&page=8&count=78
http://vip.asus.com/forum/view.aspx?id=20110101010416253&SLanguage=en-us&board_id=21&model=Xonar%20Essence%20ST&page=1