I don't happen to know anything about which places accept what from where, but can you find anywhere that sells Amazon
gift cards which accepts payments from Iraqi Visa cards/payment methods of whatever type?
Gift cards are sometimes used as part of a VPN scheme to use the US storefront from places like the UK, so if you can somehow get an Amazon gift card, that should be that solved. What you'd do is pretend to Amazon that you are an American, with a new account that uses an American shipping address (real, because they may catch on to fake addresses

, but it probably doesn't matter if it is someone else's address if you never ship physical items) and then connect via your VPN to Amazon. You may not want to connect your Kindle to WiFi unless, say, tethered to a smartphone that is using a VPN*. And for obvious reasons a 3G Kindle would not be a wonderful idea.
EDIT: Come to think of it, I wonder if Amazon themselves will sell you a gift card at least, with an Iraqi Visa. (From a different account).
* It should also be possible to have your WiFi router act as a VPN gateway, using the magic of dd-wrt or something. Not that I have ever looked into the issue, but GoogleFu implies there are a few things you can do.