To get Flash working in Chromium, you can use the Pepper Flash Player installer (Pepper Flash is extracted from Google Chrome), which is available in the official Ubuntu 14.04 repositories.\\
To install..
<code>
sudo apt-get install pepperflashplugin-nonfree
sudo update-pepperflashplugin-nonfree --install
</code>\\

For Ubuntu 12.04 (trusty), you can use a PPA
<code>
sudo add-apt-repository ppa:skunk/pepper-flash
sudo apt-get update
sudo apt-get install pepflashplugin-installer

Terminal Commands:
sudo add-apt-repository ppa:skunk/pepper-flash
sudo apt-get update
sudo apt-get install pepflashplugin-installer
echo '. /usr/lib/pepflashplugin-installer/pepflashplayer.sh' | sudo tee -a /etc/chromium-browser/default
</code>