I have the same problem. It has started quite recently. When I attempt to open certain web sites, one for my church, for example, the opening page of the website appears for a second or two and then a small window appears that says:
"Update your Flash Player in order to continue
"The version of 'Adobe Flash Player' on your system does not include the latest flash update and has been blocked. To continue using "Adobe Flash Player", dowload an update version."
And then there are 3 buttons to click on: Restore Update OK.
Assuming that clicking on " Update" will make things right, I click on it. A few things happen. I then try again to open the website but the same window then appears with the same message about the need to update Adobe Flash Player. I have twice contacted Adobe support and they have pointed me to an Uninstall Flash Player site and I have gone through that procedure to no avail. They also have asked me to open System Preferences on my iMac (MacOS Catalina version 10.15.4) and click on the Flash Player icon. The problem there is that there is no Flash Player icon in the System Prefences window. Learning that fact, the support agent seemed to suggest that what I am dealing with is not a "legitimate" Adobe Flash Player. I have tried to solve the problem by sending to Trash all of the Flash Files that I can find, but that has not solved the problem either.
[moderator: edited title after moving to new discussion topic]
I moved your post to a new discussion topic as it's different from the topic you posted to.
Can you post a screenshot of the notification you're getting?
Official Flash Player update notification doesn't have a 'Restore' option. Only 'Remind me later' or 'Download'.
Here's a screenshot of the official Flash Player update notification:
They also have asked me to open System Preferences on my iMac (MacOS Catalina version 10.15.4) and click on the Flash Player icon. The problem there is that there is no Flash Player icon in the System Prefences window.
This further confirms that whatever is being installed isn't the offiical Flash Player installer as Flash Player installer includes the Flash Player Settings Manager in System Preferences, allowing the user to modify several security settings and check for an update. Here's the System Preferences with the Flash Player Settings Manager icon: