They are downloading without my consent. The message screen pops up and the download starts automatically.
That should not happen. Check to see if you have any settings in your browser to stop that. In Safari, on the General tab, make sure that "Open 'safe' files..." is NOT checked. They might be loading something in an image file (like the "warning" itself).
The odd thing is that this is coming from a legitimate new site - Real Clear Politics - which I browse every now and then. Or, perhaps, coming from one of the news sites that it links to. That is what makes this so strange. I make a habit of never visiting dangerous sites, so I don't know where this might have come from. I am losing hope and making a Carbon Copy Cloner backup of my system getting ready to do a factory reset if it comes to that. I got used to doing that with Windows systems but I did not expect to have to do so with a Mac. Live and learn.
It's not the site, it is much more likely the advertisers on the site over which the site has little control. Websites often don't have specific advertisers, but sign up for a service that puts ads on the site that are supposed to be "appropriate" to the site. A maleficent ad can link to link to link to get to the bad stuff it wants to put on your system. And the ads on those sites are rotated, so even if you report it to the site owner, it may well be gone before the owner can even check it out. Bottom line, don't ever click on a popup to install anything, in particular Flash.
You said you got rid of the panel on System Preferences. I don't think that uninstalls Flash, just removed the support from System Preferences. Maybe what you should do at this point is to go to Adobe directly, find the Flash installer. Download and install it, then go through the proper uninstaller to remove it. That should get rid of any residual files and clean up the system from any debris left behind.
Also, DetectX Swift is a really good malware detector, so run that and clean up what it identifies until you come clean to get rid of any malware that crept in with these bogus installers.