In order to set this up follow these directions
Open the Amazon Alexa app
Tap in the upper-left corner (three lines)
In Alexa Preferences make sure to select Music.
Tap Link New Service.
Tap Apple Music.
Tap Enable To Use.
Follow the instructions to sign in with your Apple ID.
Enjoy Apple Music through Alexa.
Embedded below is a 1 minute and 56 second YouTube tutorial.