Experiencing enormous noise when initiating Bluetooth headset call mode on iPhone
I had the exact same problem and reached out to Slack support.   Got this reply

Thanks for writing in with those details, and sorry you're not able to make any hands-free Calls at the moment!
Unfortunately we don't yet support bluetooth connectivity on iOS devices -- that's only available on desktop for now.
That said, full support is in the works! I don't have an ETA to offer right now, but please trust that the team are working on freeing up your hands!

So surprisingly it looks like bluetooth support is app specific not iOS specific.