The reason for this is that Google have dropped support for the ‘Netscape Plugin API’ (NPAPI) – used by Adobe Flash – on Linux builds of Chromium. This ageing plugin allows for unrestricted access to a computer and is considered inefficient and insecure, with Google calling it ‘the leading cause of hangs, crashes, and security incidents’.
To install the new Pepper Flash plugin (which now comes with Chrome) open terminal and type.
sudo apt-get install pepperflashplugin-nonfree
sudo update-pepperflashplugin-nonfree --install
Restart Chromium and Flash will now be working.