That's very odd. If you have a 64-bit OS, the FlashPlayerApp.exe utility would be saved in C:\Windows\SysWOW64, not C:\Windows\System32.
What windows version do you have?
Can you try performing a clean installation of Flash Player? See How do I do a clean install of Flash Player - Windows?
I have Windows 10 Home, 64bit x64 processor. I tried copying the FlashPlayerApp.exe file from another location and pasting it into the system32 folder but the icon in Control Panel still does not work.
If the file should not have been there then what would cause it to be placed there?