oh glad its not just me! I've been having the same issue since I updated to Monterey (2018 Intel Mac mini). using 2.1.0 I try to add a button to my Mac. The flic / App seem to be connecting and pairing (the flic button switches to green) and the App says the usual "Found one, connecting". but then the process just kind of hangs there. Shortly after pressing the flic returns to its unpaired orange blink. In my case I do not believe this is an issue with the button being paired to another device. I can pair/unpair from my iPad and iPhone with no problems (including the 'forget this device' step in bluetooth). Other things I have tried that never seemed to work was the usual, 'sudo pkill bluetoothd' and restart, deleting com.apple.bluetooth and restart, booting in safe mode, and resetting the SMC. Of course Apple has removed the debug and logging options from the bluetooth menu via 'option + shift'. so its anyones guess as to what is actually happening. There was also a 'factory reset' of my flic button too, but also to no avail.
I personally don't believe that the FLICTEAM has tested their products in the US with the latest versions of macOS, but that's just my opinion.