This is really cool. It reminds me of Sococo but way more integrated with the tools out there. Any chance I could give it a try?
What happens when you click the slack button in the team list? You can send a direct message to that teammate?
If you hit the Slack button it opens a link to that Slack chat. If you are in a room with a group it'll open a group DM to the other people present. (I personally rarely use the Slack button because any given DM or channel in Slack is only ever alt+tab and ctrl+k away, but that's just me.)