RQM and Slack integration
One answer
What you really need are webhooks. Unfortunately, that's not something that QM has right now, though internally we've floated the idea and Slack integration was one of the use cases we thought of when discussing it (we also use Slack). One of our big questions around this is whether or not there is demand for such a thing. I've dumped some of our thoughts into provide webhook framework for integrating and extending QM (167869) and would encourage you to register your interest there.
Without webhooks, your next best option is to poll QM using the Reportable REST API or OSLC API as described in the link above.