Install flash using the following command
sudo apt-get install flashplugin-nonfree
Now you need to copy libflashplayer.so file into /usr/lib/chromium-browser/plugins directory
sudo cp /usr/lib/flashplugin-installer/libflashplayer.so /usr/lib/chromium-browser/plugins
Now you can run the chromium browser using the following command from terminal
chromium-browser --enable-plugins
or
Go to Applications->Internet->Chromium Browser and right click it, add to panel.Right click the new chromium icon and add the following command where it says command
chromium-browser --enable-plugins
