The problem is not downloading it, it is installing it. It simply will not install. Anyone have any suggestions?
The system information in the thread Pat referenced above would be very helpful in understanding what's happening.
My guess is that you're running an old version of Safari. Apple and Adobe want everyone to pick up an important security update, so Safari blocklisted old Flash Player versions. This is why you're seeing the blocked plug-in message.
It sounds like you're completing the installation successfully, but Safari doesn't know that the latest version is installed. I'm *not* seeing this on any current versions of MacOS or Safari, and I'm trying to figure out which versions are affected. If you could let us know, that would be great. If you don't know how to get that information, we'd be happy to guide you through it.
Once you get the version information, please run System Update on your mac (the Apple in the upper left of the screen > System Update) to see if maybe there's a new Safari version waiting for you. If so, please download and install the available update and let us know if this resolves the blocked plug-in issue for you.