"You can't open the application 'Install Adobe Flash Player' because it is not responding.

Here's my recommendation:

First, let's get you to a good baseline, and make sure that any latent problems with the underlying operating system that might be preventing us from installing are dealt with.

If you haven't made a backup of your computer, it's always a wise idea before giving it a good workout with system maintenance, especially if you have photos or documents that you can't replace.

Once your backup house is in order, let's check for and repair any latent problems with the filesystem, and repair any filesystem permissions that may have become corrupted over time.

See the "Try Disk Utility" section:

https://support.apple.com/en-us/HT203176

While you're there, choose Repair Filesystem Permissions (Verify will frequently return clean, but then Repair will still fix a bunch of problems).

Once that's done, let's uninstall Flash Player from your computer completely.

Uninstall Flash Player - Mac:

https://helpx.adobe.com/flash-player/kb/uninstall-flash-player-mac-os.html

Once you've done that, shut down the computer from Apple > Shutdown.  Let it sit for a few seconds to allow all of the hardware to fully discharge and reset, then power the computer back on.  This eliminates a whole bunch of unlikely-but-possible causes of problems, which, should you run into trouble, makes figuring out what caused it much more straightforward.

Once the computer is back up, download a pristine copy of the Flash Player installer from here, and run it.

http://get.adobe.com/flashplayer/

If it still fails, please give me the logs so that we can fix it, and then try the alternate set of installers.  They'll probably get you going, and we can do the forensics and try and handle whatever is going on in future versions of our installer.

https://helpx.adobe.com/flash-player/kb/installation-problems-flash-player-mac.html

Collecting and posting the logs would help us improve the product, and the links to the offline installers at the bottom of the guide should get you going.

Thanks!