Tor Browser does not support external plugins for security reasons. External 
plugins such as Java and Flash as full-fledged programming languages with no
proper sandboxing can read sensitive local information and make outgoing
connections without obeying the proxy settings in your browser. We are working
on a properly sandboxed Flash.

Youtube offers HTML5 video for many videos, which works fine in Tor Browser: 
https://www.youtube.com/html5