So you know how currently a flag is immediately seen by the entire 10k+ rep users community and all the mods in every room. That's not right.
What I'm proposing:
When a flag is raised, at first only the room owners can see it and review it, in the spirit of self-moderation.
If the room owners are away from keyboard or they choose to not make a decision after 2-3 minutes, or if there are no room owners in a room, the flag goes up to the moderators of the site to which the room is related.
If these local mods aren't there to handle the flag in 2-3 minutes, it goes a tier higher to all moderators. And if they're too busy, they may choose to forward it to all 10k users as it's currently working.
Flags raised by room owners go to local mods, since if they placed it, they are not able to handle it themselves. (or if the granular room owner privileges/abilities are implemented, to other room owners who have the privileges required to handle chat flags)
At any point the flag reviewer may hit the "I'm reviewing this" button which will extend the timeout after which the flag is taken up a tier (maybe by extra 5 minutes), so that if nobody is reviewing it, it goes up faster. (I don't know if that's going to be necessary, but just in case I decided to include this idea)
All raised flags and their review results are visible to moderators in the chat room's flag history (we're gonna need a page for that). Mods can review them and if some room owners are abusing the flag review system by snuffing them out when it's not appropriate (from what I've read, this happens and needs to be considered), these users may lose their chat flag review privileges across all chat rooms. So if a flag is raised in a room where there are only "untrustworthy" flag reviewers, it goes straight past them to local mods.
(I already posted this as an answer and in comments to "We're more aggressively enforcing self-moderation in chat" discussion, but I think it deserves its own place now that I've fleshed it out enough.)