Unfortunately the bugs in Flash extend beyond the player itself, as I learned the hard way while trying to update a handful of machines to the latest version.
If the firewall is not configured appropriately it may stall the download/install operation of Java under certain conditions.
Refer to your specific Internet firewall manual for instructions on how to disable your Internet Firewall. Starting with Java 8 Update 20 (8u20), on Windows systems, the Java Uninstall Tool is integrated with the installer to provide an option to remove older versions of Java from the system.
The first three machines I tried this on resulted in three different outcomes, and the software was not removed on any of the machines.
Instead, Adobe has an uninstaller for the Flash player.
I dutifully ran the Adobe Flash uninstaller (the version from December 3, 2007) and then went back to the tester page to see what it had done.