I think I have found a solution to the problem that allows the built-in chrome version to run with the system version without conflict. The answer is to download and run the STANDALONE version for Internet Explorer that does not work in Chrome.
Type: about:plugins in Chrome address bar and if you see 3 files relating to shockwave follow these instructions:
Disable the version that says “pepperflash”. This is an experimental one that’s not needed.
Download Revouninstaller Free and install it;
Uninstall all instances of flashplayer and shockwave with it.
Again type about:plugins in Chrome’s address bar (Press Enter) and you should only see now “pepperflash” entry (disabled in picture below) and Chrome version (two files). Like here:
Download these versions of the shockwave and normal flashplayer and install them.
Note: It would seem that the “Shockwave” entry in “about:plugins” actually means the normal flashplayer but I removed both types with Revo just to make sure and reinstalled versions of both that are not compatible with Chrome.
If you need Flash for Firefox, Opera etc as well go here (Download in that browser):