Best answer by Ken_Griffiths
Are you asking how to play Amazon music from the Amazon App itself direct to your Sonos One, if so, that is not currently possible? If you use iOS then it will be possible when Airplay 2 is released by Sonos sometime in July 2018.
Meanwhile if you are a Prime or Unlimited AM user, you could install the Amazon Music Service in the Sonos App and launch tracks to your speaker from the service within the Browse Tab.
And/Or you could install the Sonos Skill in the Amazon Alexa App and link your Sonos Account to Amazon and play their streaming music service via Alexa voice control on the Sonos One.
You will find plenty of information to get you started with all these things in the help section of the Sonos App and also in the community help/support pages. Here are a couple of links to help get you started...
Setting up Amazon Alexa on Sonos
How to add a music service to Sonos
Using AirPlay with Sonos