@Emil I was getting the "This Device is not supported" message while trying to set up my first routine in Alexa as well. After some troubleshooting here is the workaround I found.
Assuming that you have already enabled the Flic skill within the Alexa app:
- Open "Devices" menu in the Alexa app and find your Flic
 - Delete/Forget the device
 - Fully close the Alexa app. (It shouldn't be running in the background either)
 - Fully close the Flic app. (again, it shouldn't be running in the background)
 - Open Flic, set up the button to trigger Alexa if you haven't already.
 - Open Alexa and click the button - it should say, new device discovered.
 - DO NOT CHANGE THE NAME OF YOUR BUTTON IN ALEXA
 - Create a routine and start from the bottom, i.e. Actions -> Triggers -> Name.
 - Now it should work successfully.
 
This worked for all three of my buttons so hopefully it works for others as well.