If you tap the Casting icon in the Amazon Music app, you should be able to select the Beam as your device to play music. If you have an iOS device, you can also AirPlay the music to the Beam under this same menu.

Thanks Rashi. Unfortunately it says "cannot find device". I'm using an Android phone. I have no problems connecting with Pandora or Spotify. 

Be sure the Sonos skill is enabled in the Alexa app.

https://support.sonos.com/s/article/3248?language=en_US

https://www.amazon.com/gp/help/customer/display.html?nodeId=GMBKJXSDC5EWSRJH

I don't want Alexa enabled. I just want to cast like any other app/service. 

You don’t have to use Alexa. You just need to enable the Sonos skill in the Alexa app. You won’t be able to cast from Amazon Music without doing this.
 

How do I control Sonos from the Amazon Music app?

You can control Sonos directly from the Amazon Music app by following the steps in Amazon’s article about casting. Note that the Sonos skill must be enabled in your Alexa app, even if you are not using Alexa with Sonos.

Essentially, Amazon casting and Alexa voice assistant are using the same authorization and cloud services to send audio commands to Sonos.  Alexa commands to Sonos were implemented first, and if I remember correctly, Amazon implemented casting to Sonos and didn’t even really involved Sonos in the testing.  Same thing, so no testing really required.

Thanks for everyones input. I got it working unfortunately casting using the 'skill' is slow between songs. Also you can't group speakers through the Amazon app. I'm going to stick with Spotify.