For Chromium browser versions greater than 34, to use flash one must install Pepper flash.
For Ubuntu 14.04 or newer, run
sudo apt-get install pepperflashplugin-nonfree
sudo update-pepperflashplugin-nonfree --status
# to see what version of Pepper Flash you have installed.
sudo update-pepperflashplugin-nonfree --install
# If there is a newer version available
For old users, you can run the below commands to add the PPA and install Pepper flash in any Ubuntu version above 12.04
sudo apt-add-repository ppa:skunk/pepper-flash
sudo apt-get update
sudo apt-get install pepflashplugin-installer
To configure Chromium to use Pepper flash,
# open /etc/chromium-browser/default
. /usr/lib/pepflashplugin-installer/pepflashplayer.sh
# add the above line to the end of the file on a new line and save.
Close all windows and re-open to make the installation work.