I'm having issues too. I can get Alexa connected and it provides weather info and answers questions but it will not play my prime music through it.
I think it may have something to do with the fact that only certain services are available via the free data connection and for anything else you need to purchase a data plan. I have seen something in the manual which seems to indicate that you can use your mobile device for the data connection but it is very vague.
I have an Android and an apple device so I am going to try with each device to see if I can get it working.