I got an Amex gift card a few months back and used it with no issues on amazon. Well I take that back I had a couple issues:
First, I attempted to structure my purchase to use the whole card in one shot (leaving less than $1 on it). Amazon put a hold on it for $1 then tried to hit it with the full price and it was rejected. I had to drop an item from my cart and then place the order.
Second, because not all my items were sold by amazon the first process got repeated a few times. I ended up needing to buy a $2 gift card for myself to get everything I wanted (see below).
All of the concerns posted here were non issues for me. I added the card with my own name and address as the billing info. I had to return items in that order so I even had credits back to the card - again, no issues.
Just be aware of the holds amazon will place and plan accordingly. You can't split payments but you can use gift card balances - So buy yourself a gift card to cover the difference, apply it to your account, then use the Amex gift card.
It all works if you do it right.
Viper GTS