http://cae2100.wordpress.com/2012/12/23/installing-flash-player-on-raspberry-pi/

Installing flash player on Raspberry Pi

We all want to do stuff like play youtube videos and such, but due to the closed source of adobe flash, we are unable to do this on the raspberry pi. We’re all in luck tho, the open source alternative named Gnash is here to save the day! Here is the two commands you need to open to get flash player working in Midori, which is the default web browser in raspberry pi.

First, open a terminal and type:

sudo apt-get install gnash

sudo apt-get install browser-plugin-gnash

and close out of terminal, then make sure you restart your browser if you have it open. Then go have fun with watching your youtube videos. Easy as that