On Windows 8 and higher, Flash Player is a built-in component of Internet Explorer. Updates are managed directly as part of Windows Update. There's nothing for you to do.
It sounds like you're running into a graphics driver bug. Graphics drivers take a long time to fully mature, and Win8 is relatively new still. Also, most YouTube videos served to Internet Explorer users on Windows 8 are HTML5 videos. You can confirm whether or not the player is using Flash by right-clicking on the movie. If it says About Adobe Flash, it's us. If it says About HTML5, it's not.
Here are some instructions on disabling hardware acceleration that apply to IE11:
How to enable or disable software rendering in Internet Explorer 9
If you're still stuck, it would be helpful to get detailed information on your hardware and drivers. This will help us reproduce the issue and report it to the appropriate vendor, etc.
Open a command prompt
Type the following:
dxdiag
Hit Enter
This will launch the DirectX Diagnostic Tool
Choose Save All Information. Paste the contents of the file (or a dropbox or pastebin link if that's easier) to this thread.
Thanks!