I know that adding moderator flags to the iOS app is on the roadmap from the answer to Please add diamond flag handling to the iOS app. This is a supplemental feature request that I want to get into the request queue for when mod flag handling is ready to be tackled.
Getting a notification of a new flag would make flag handling quite a bit faster. Handling flags in a timely fashion is part of why we have multiple mods. Being able to improve flag handling without adding mods would be a nice efficiency perk.
Obviously it can't be an always-on feature though — SO mods would mutiny, to put it mildly. It would be extremely useful on the many smaller SEs though, where flags are a few a day and swift handling makes a disproportionately significant improvement in site quality. For it to be a reasonable feature, it would have to be a default-off switch.
Could we have a flag notification feature in the iOS app, which is default off but can be toggled on, once mod flag handling is added to the app?