Here's my suggestion for the situation:
We should disable 10K user flags in the chat as they're broken anywayas they're broken anyway since they bear no context and I'm not sure I trust most 10K users to be good judges in this case. Mod flags are always there in cases of abuse.
Instead for the 'keeping the user outside of a chat' use case - implement Shog's suggestionShog's suggestion and let room owners kick users from a specific chat room. This type of system should keep us covered from most types of users who disrupt the chat. Most of the conversation in the chat is quite nice and of high quality, it's a good gathering ground to discuss interesting questions in SO and help users with questions too small to consist of a SO question.
We've build something that does this outside of the system in the JS room and I'd like to share what we learned from this experiment:
Some problematic users just don't understand the system - the first 'kick' should remove the user from the room and show them a help screen like Shog suggested. A user may rejoin the room immediately after reading the help text. We're found out that (surprise surprise) kicking users is really antagonizing to them. If talking to them doesn't help initially or they don't understand what they're doing wrong - this should serve as a strong indicator.
There should be no 'stigma' here and this should be a step designed to help the user understand the system better. People easily get antagonized by hostile behavior from a community and can turn into problematic users quite fast.
Some people are genuine trolls or help vampires - those people are not looking for constructive discussion. Sometimes people want to test their boundaries. The 20 rep limit really helps cut down the noise here, but there are a lot of people who come to the room, ask for help, and when they're told to do their own research before asking start acting in an abusive manner. The second flag should last 30 minutes so the user has sufficient time to cool down.
It should be made clear to the user that they can correct their behavior at this point and become constructive members of the community.
Some people are repeat offenders - we've had random people we don't like join the room and for weeks make sexist remarks that border sexual harassment, racist remarks, and hateful remarks. Telling them they're not welcome members of our community didn't help very much. Upon a third kick a mod flag should be raised and the user should not be able to join the room until a mod has reviewed the flag or for the very least for at least an hour.