If I try to limit access websites in screen time OK is greyed out.

I see. I don't think screen time will solve the pop-up issue, but we can try. Images can be uploaded by pressing this icon in the editor toolbar:

I'd recommend trying an ad blocker, such as AdGuard for Safari (free and open source), this can potentially get rid of annoyances like that.

Another thing worth checking out are the settings in Safari > Preferences > Websites, there are options to allow or block notifications and pop-up windows for various websites.

The Done button is greyed out for me as well, but only until I enter a time greater than zero in the Time field.

Set time limits for apps and websites in Screen Time on Mac – Apple Support

If the guide didn't help resolve the issue, can you take a screenshot?

I see you're trying to block the website using Screen Time > Content & Privacy > Content > Web Content. I don't think that's the right approach. If I'm understanding it right, the second screenshot is the Limit Adult Websites setting's customization dialog, which does this: "Automatically limits access to many adult websites. Click Customize to enter additional allowed or restricted websites."

The Web Content restrictions will block whole categories of services, this customization dialog is meant to further fine-tune that, it's not really for defining unrelated blocking rules like the pop-up we're trying to get rid of.

I recommend trying these options instead, like I posted above:

I'd recommend trying an ad blocker, such as AdGuard for Safari (free and open source), this can potentially get rid of annoyances like that.

Another thing worth checking out are the settings in Safari > Preferences > Websites, there are options to allow or block notifications and pop-up windows for various websites.

If you can include any information on the "Your flash player may need to be updated" pop-up, maybe a screenshot or the URL where it appears, that would also be helpful.