Can you watch it on an iPad? (An iPad has never used Flash). If so, switch on the Develop menu (under preferences>advanced) and then use it to change the user agent to iPad. The web site will think that's what you're using and deliver the HTML5 version it uses for iPads.
This may not help but... YouTube "just works" here on Safari/Mac and has for a long time. I thought they had long since re-encoded all their videos (probably driven by the whole iPad/iPhone thing).
I haven't had Flash installed for years: too much maintenance and too many security issues.