While I haven't read through the entirety of the recent discussion regarding
Lounge <C++>, I've read enough to (IMHO) reasonably conclude that there's two large issues at work there.
People who are having their activities moderated need to be more civil about it, lest they be even further moderated.
Chat moderation on StackExchange could use a bit of tweaking, to reduce the likelihood of outside users performing moderation that may not fit the current context or culture of the room.
The first isn't really something we can do much about - people who don't want to be civil (whether it be in general, or simply in certain situations) just won't. That's one of the reasons moderation exists in the first place.
However, I think there are some appropriate changes that can be made to address the second part.
Outside users may not be able (or simply may not be willing) to perform enough depth of review to put flagged content into its proper context before acting upon it. However, the room's current (or recent) participants are probably very familiar with the context and therefore logically the most appropriate people to pass judgment.
Given this, the most logical move (at first glance) may be to entirely restrict chat moderation to only the participants of the room. However, this could become a problem where there are not enough moderators or high-rep users (I'll collectively refer to these as "flag handlers") present to deal with flags within a reasonable amount of time.
However, if there are enough flag handlers around, why not give them a chance to handle the issue internally before getting all of the StackExchange flag handlers involved? This reduces flag noise for non-local flag handlers, increases the likelihood that context and local culture will be taken into account before a flag is handled, and still leaves the entire SE flag handling community available to handle flags that the local users can't deal with on their own.
Immediately when a flag is posted to chat.
Notify local flag handlers only. "Local" includes any flag handlers currently showing as present in the room. May also want to include any who are currently active elsewhere in chat, and have visited the room within X days. (I'd say X probably shouldn't be more than a couple weeks.)
After a delay, only if the flag has not already been handled.
Notify non-local flag handlers. I'm thinking somewhere within 1-2 minutes would be an appropriate delay. Certainly no longer than 5 minutes, and no shorter than 30 seconds. Maybe consider throttling the delay according to recent flag volume. (i.e.: More flags per minute across the past X amount of time - say, 15 minutes to an hour - means a shorter delay.) Also may want to consider eliminating this delay when the room has a low number of "local" (or recently-local) flag handlers available.