Sorry for picking up an old topic but I feel like I need to answer this, since I was trying to solve their damn pin verification problem for days.
I've spend a couple of hours looking for a free service capable of providing US number receiving call from Amazon. Obviously there are a lot of cheap paid options, but I knew there should be one free.
And I found textnow com. I know that a lot of folks here already know it, as sms receiving service among dozens of others, but this is the only one I found which is able to provide US number (free!) receive a real phone call and you can even type the PIN right in that service using their web interface.
I didn't activate my Amazon account yet using this, but I was able to receive a call from them and successfully enter the pin - it's just that I already spent my activation attempts on that time and decided to try later. But it really seems that it works. Will post here later with final verdict.