Flash is a sometimes annoying piece of software and in no means a critical Windows component, so:
NO, don't re-install!!!
Just press the direct-link to the official Flash Uninstaller here: Direct Download Link
Or find it on the official Adobe site here: http://helpx.adobe.com/flash-player/kb/uninstall-flash-player-windows.html#main_Download_the_Adobe_Flash_Player_uninstaller
Save it to your desktop, close down all applications, and double click the file you just downloaded.
That will un-install the Flash you have on your system. Reboot and the problem should be solved.
Optionally, after you are sure it's solved, you could re-install the latest version of Flash right here: http://get.adobe.com/en/flashplayer/
But most software and applications run fine without it, so only do so if you're sure you even need it.