sudo apt-add-repository ppa:skunk/pepper-flash
sudo apt-get update
sudo apt-get install pepflashplugin-installer

Note that you need to configure Chromium to use Pepper Flash. To do this, open /etc/chromium-browser/default and add the following line to the end of the file on a new line:

. /usr/lib/pepflashplugin-installer/pepflashplayer.sh

Close all windows and re-open.