I never had any problems using a foreign credit card at Amazon, but I do use a US VPN most of the time, just to be on the safe side. The only place it doesn't work is for the digital download services.
If someone really needs a US credit card with a US mailing address I suggest
www.usunlocked.com. I have their card, and it works everywhere I tried it. I don't use this at Amazon, because there is an extra charge for using this card, so I only use it when it is necessary.