One of the bigger complaints against Linux is that Flash performance does not seem to work as well on this operating system compared to others. There still is not full screen Flash support which has been an issue for a few years now that still is not fixed. While flash is not the most efficient plugin by any means as it dominates CPU and Ram, there are still some things that can be done if you want to get better performance out of Flash on your Linux system.
Some prefer using the open source version of Flash. This is because of personal beliefs about the freedom of software. The open source version does not work as well as Adobe's. If you are suffering from poor performance, consider switching versions of the Flash plugin to the version that works a bit better on Linux systems.
If Flash is using too many resources, then that means you need to free some up on your system. One way of doing this is using a different graphical user interface. Switch to something that uses Fluxbox or XFCE or at least try and turn off extra desktop effects that are not really needed.
Update your browser to something new and make sure that you do not have too many extensions that are slowing it down. At times poor Flash performance is an issue with the browser versus the plugin.
One option is to disable other Flash objects on the page. At times when running a video, for example, there might be two or three banners around it running Flash as well. All these together can cause lag. If you get an ad blocking browser plugin, you can turn those banners off and just focus on the Flash objects that you actually want to view.
If you need to, consider downloading the Flash objects and running them by themselves. There are many SWF and FLV players that will flawlessly play Flash even at full screen on Linux which will work fine.