aaronlbpeterman do you want that in Flarum or at FreeFlarum's website? If you want this in Flarum, you should make an extension/feature request to have that added - it's definitely possible to fire notifications with extensions, and it should also be possible to make custom alerts (at least by modifying the current Flarum error box's CSS)
As for FreeFlarum website alerts, I have already made a small bottom popup for messages (in rebase, so not live yet), but that's just for errors that happened at the moment/in real time (e. g.: invalid value was entered in a form).
We don't plan to make an user notification system like Flarum's (for https://freeflarum.com/settings for example) because FreeFlarum is built with Python, and making it communicate with Flarum's PHP listeners to fire notifications is impossible. We could make it connect to the database to fetch data, but that's another tedious thing to do (we'd have to make FF check for new notifications every so often, check if there are new posts since x date, etc...). It's unnecessary for FreeFlarum to have this, as Flarum already can handle this