I am a developer that recently got a Samsung Gear S3 with LTE smart watch and in reading up on developing for the watch I have come across a few things.
It looks as if for Alexa to work (as of 3.1), the headphones pipe Alexa commands through the Bragi app and then into the Alexa app. I feel like this is unnecessary. A cursory look a the Alexa API makes it seem as if they have a direct way for devices to communicate with their server (sans App).
It would be nice if:
A. The Bragi App went around the Alexa app to work with Alexa.
B. Even better, the Bragi Headphones got internet access by way of proxy through your phone (just like the Samsung Gear S3 and probably many other smart watches) and talked to Alexa that way.
The reason I bring this up is because the interface to Alexa does not seem to always work.