Yeah, this is normal. MacOS has been tightening things down over the years with regard to appliication installation (i.e. funneling everything through the App Store), but Flash Player isn't a traditional desktop application. We're a browser plug-in. Recent MacOS updates require additional permissions to run our installers and uninstallers, which is why MacOS is asking for your password. The goal is to create a speed bump so that attackers can't silently add or remove critical system components.
Anyway, if you have any doubts about the authenticity of a pop-up or application, validating the digital signature on the corresponding executable is the authoritative way to confirm whether or not it came from a reputable publisher, and has been unmodified since it left their build systems.
The easier path is to simply download a new copy of the uninstaller from a trusted source. When in doubt, better safe than sorry.
You can get our uninstaller here:
Uninstall Flash Player - Mac:
https://helpx.adobe.com/flash-player/kb/uninstall-flash-player-mac-os.html
Uninstall Flash Player - Windows:
https://helpx.adobe.com/flash-player/kb/uninstall-flash-player-windows.html