Operating system is most recent OS X El Capitan 10.11.5 . It's done this on previous mac OS's as well. When it didn't work through the update, I uninstalled it to try a fresh install and that gave me the same error. So, now I have NO FLASH working AT ALL!
This is the OS prompting for the password, therefore, this is the password you use to log into your system (assuming it's an Admin password as Flash Player requires Admin permissions to install). If you don't have a password, you can leave most likely leave it blank and click OK to continue.
For more information, including links to how to reset your computer password, see What userid & password do I need to install Flash Player?
I'm using the right OS password. I enter it correctly, it accepts it and then when it tries to start to install, it gives the error. This has happened before, but only ever with Adobe. So, Apple has said it must be an Adobe problem. How do I fix this?