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.
It's the one that's causing your problems... rather it not being on your system is causing them.
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.