has anyone else been getting phoney update requests from Adobe Flash Player?

There are a lot of fake Flash update messages. Do not click on them. They may try to install completely different software.

If you want to update Flash, do it from the Update tab in the Flash system preference, or from Adobe's website.

Also:

https://www.macrumors.com/2020/01/23/next-version-of-safari-drops-apple-support/

Many see these fake update links for Flash Player. Only get Flash updates from the source:

https://get.adobe.com/flashplayer/

Not sure if it is still true (haven't had Flash on my system since Mojave),

but when you install the "real" Adobe Flash it also installs a control

panel in System Preferences and if you ever see that message again, just

check there to see if there really is an update.

AppleBlanchesc wrote:

I keep getting requests to update Adobe Flash Player but it does not appear to do anything and the app really wants me to remove or uninstall the Player. Any words on how to stop this notification?

This is as old as the hills.

Avoid phishing emails, fake 'virus' - Apple Support

I suspect you have installed adware/malware. Try running this trusted utility https://www.malwarebytes.com/mac/

AppleBlanchesc wrote:

You were bang on. Ran the scan and found a gremlin. It has now been quarantined. Thanks for your help.

Good computing AppleBlanchesc !