I have this "1 flag" notification icon, but I have no flags.
Not really sure what's going on here.
I think it's a flag for which you cannot decide any action. If I look at that, I see what shown in the following screenshot:
This is what happens if you have the privilege of reviewing edits proposed from other users, you are a 10k user, and you propose an edit for a tag wiki: The top bar shows there is one proposed edit, but the review page will tell you there aren't reviews.
This sometimes happens to me also for proposed edits done from other users: I refresh the page (e.g. by clicking on the "Questions" link), I notice there is a new proposed edit because the number shown on the top bar, I click it, but when I get the review page, I don't see any pending edits (and I am sure it is not one of my proposed edits).
Another explanation is that the count shown in the top bar is cached, and you see the number of flags for which an action has already been taken.
This is what happens with flags in SE sites too.