Your troubles aren't coming from Flash Player.
You're missing a file that was made visible by the 10.8.5 update. Hundreds of thousands of Mac users all over the world deleted it, not knowing what it was. It causes this when it's missing.
Download this file: "Secrets" pereference pane
And this one: mach_kernel.zip
Install Secrets, and open your System Preferences.
Open the Secrets Preference Pane, and check "Show hidden files"
You'll need to press the "Quit this" button,
and restart Finder, by right clicking the Dock icon.
Then, place the mach_kernel.zip file in the Mac HD directory,
and unzip it. You should see a "faded" mach_kernel file appear.
Trash the zip file.
Reopen your System Preferences and uncheck "Show Hidden files".
Instead of quitting Finder and relaunching it, reboot your Mac.
Your Flash Player installer won't quit anymore.
Strange, I certinly do not remember seeing or deleting any strange files. What would that visible file been called?
That fix worked perfectly. Thanks for laying it all out with the screenshots...thats always helpful.
What would that visible file been called?
"mach_kernel" is the name of it. Most people didn't give it a second thought, because it's only 3mb and it looks like a blank file. It was dumb of Apple to unhide it in the update.