I've been able to use Zyn with Jack, but when I want to watch a Youtube video, I have to close Zyn and stop Jack. Currently, I don't know how to watch a video with audio while using Zyn. Is there maybe a way to use Zyn without Jack and if so how?

If you have a recent version of Zyn (2.4.2/2.4.3) it should be possible to disconnect it from jack/whatever-other-backend-you-were-using via File->Nio_Settings (if zyn is the only jack client, then the jack server should stop when you disable jack there as well). I know that there was some initial work on getting flash to route to jack if you want another route though.