I have looked into the problem a few years ago.
My impression is that the core of the problem is that the NPAPI flash versions ended somewhere at 11.
The NPAPI version only gets the most important security fixes, but do not get developed further.
Chrome uses the PPAPI flash, which gets updated constantly and supports all the modern stuff.
This plugin is incorporated into the Linux Chrome executable.
It must be extracted (the whole thing is in some archive format).
To get it work together with Chromium, one must write a manifest file and specially archive that together with the plugin extracted from Linux Chrome.
Then you have to fiddle a bit with Chromium to accept that plugin.
I got it all that far, but the plugin still didn't work.
I am sure I made some mistake.
But on Linux many guys have succeeded.
There are nowadays even a few Linux utilities which automate the steps listed above.
My impression is that the core of the problem is that the NPAPI flash versions ended somewhere at 11.
The NPAPI version only gets the most important security fixes, but do not get developed further.
Chrome uses the PPAPI flash, which gets updated constantly and supports all the modern stuff.
This plugin is incorporated into the Linux Chrome executable.
It must be extracted (the whole thing is in some archive format).
To get it work together with Chromium, one must write a manifest file and specially archive that together with the plugin extracted from Linux Chrome.
Then you have to fiddle a bit with Chromium to accept that plugin.
I got it all that far, but the plugin still didn't work.
I am sure I made some mistake.
But on Linux many guys have succeeded.
There are nowadays even a few Linux utilities which automate the steps listed above.