Welcome to the forums! Tell us more about your hardware specs please (processor, RAM, video card, etc).
To be clear, the Adobe Flash player is an example of "closed source" or "proprietary" software. This means you cannot "tweak" the Flash player to make it run faster or better. There is no difference between the Flash player in Ubuntu vs. Debian, Fedora, Red Hat, etc, so I doubt switching Linux distros will make much difference.
Personally, I use an app called Minitube to watch Youtube in Linux; it seems to work better than streaming the video in my web browser using the Flash plugin.