It is possible to flag a message in chat. However, chat flags are handled by users in chat, not by moderators.
But occasionally there might be issues with some chat messages in rooms associated with this site which are serious enough to require involvement by the moderators. Or some chat messages might be related to some problems on the main site and it might be desirable that mods are informed about those chat messages.
What should be done if there is a need to bring some chat messages to the attention of moderators of this site?
NOTE: I have originally posted this answer to a separate question - however that question is about multiple issue. I suppose that if this is posted separately, there is a better chance that this might be useful. (And I should probably have done this in the first place. I apologize for unnecessary noise caused by two separate posts.)