Anyone using Chrome (or a Chromium browser) that's newer than 50.0.2661.75 (last version of Chrome that still allowed NPAPI flash player) can't do anything about the latest update because all Chromium based browsers newer than the one mentioned above have their own pepperflash (PPAPI) installed and it updates automatically (version 50.0.2661.75 was the last to support flash. It's best to also go to chrome:plugins and disable the PPAPI version and leave the NPAPI enabled.
To check your version, click on the gear icon (may be the hamburger icon now, don't know) and scroll down to "about chrome" (mine is about slimjet) and it'll tell you what version you're using. The latest version of Chrome is 67-something, I believe.
They would need to need to try a different browser or uninstall Chrome and reinstall an older version. Then, uninstall flash, reboot, and download the zip file for the older flash version. Open the zip file, scroll down, and click on the first thing that says "windows installer package". The zip file is large (422 mb) but once you have flash re-installed, you can delete the zip file.
If you're using Firefox browser, you'll need to do the uninstall and re-install from the zip files found in Champion's link.
Just open the flash box in the game client, or play now button and click on "updates" to see if your flash is version 30. If it is, that's the problem.
filehippo.com has older versions of browsers and is a safe site.
Or, try Maxthon. Don't know anything about the browser, so you'll have to follow someone else's advice on that one.