Latest Flash plug-in keeps failing in Mac Safari and Firefox

It would be helpful to get some more details on what's happening, including specific versions of the OS and browser, and a few links that used to work but are now problematic.

https://forums.adobe.com/message/5249945#5249945

You can revert to the Extended Support Release, here:

Adobe Flash Player Distribution | Adobe

You'll need to uninstall first in order to move to an older version:

Uninstall Flash Player | Mac OS

If it's also exhibiting the same problem, it might just be problems with the filesystem.   Please check the disk for errors, repair any problems discovered, and run repair filesystem permissions (verify will often times return clean, but repair will fix a bunch of problems anyway).

Caveat: Sometimes corrupted software is an early indicator that your disk is going bad.  It's wise to ensure that you have current working backups, especially if you have anything important on the machine.  Checking the disk for problems is a relatively safe operation, but will also give the disk a workout.  If it's on it's way out, you may not get a lot of additional warning.

https://support.apple.com/en-us/HT203176‌

After that, do a clean install of Flash Player:
How to perform a "clean install" of Flash Player in Mac OS X

If you're still stuck please let us know.