I downloaded the Kindle iPhone app from the (US) appstore and logged on with it.
Then I went through the cumbersome process of selecting a book an buying it (the app needs in-app buying of books!).
After going through all the steps, and after choosing the iPhone as device to send the book to, I get the following geographical restriction error.
Screw you, amazon. And screw all these region specific limitations. This is the internet! (this goes out to you too, Hulu and Apple)