Welcome to Mac-Forums again.
More questions than definitive help at this moment. Sorry.
First off, from where were you downloading Flash Player? One should only download from Adobe's own site. Or, if updating Flash Player, the best way is via System Preferences, click on Flash Player > Updates.
I'm afraid there are a lot of dodgy sites out there that claim to offer Adobe Flash Player.
Next, knowing which Mac model/year and especially which OS, would assist. And which browser please?
I presume that you are not being allowed to Force Quit?? Click on Apple Icon in Menu Bar > Force Quit > choose your browser from the list and force quit. Which brings us to the fact that your download must be via a browser.
So, a possible solution is as follows:
Turn off WiFi and/or remove Ethernet cable from Mac — ie totally disconnect your Mac from the internet.
Now try force quit of browser.
Reboot. Open browser and delete history.
Reconnect Mac to Internet. If using Safari, hold down Shift Key and open Safari.
These suggestions might vary depending on your answers to the questions above, but try them out and please post back.
Ian