not to sound blasé or anything, but i didn't think this was that big of a deal.
i have bought books from .com, .co.uk, even .co.jp (although .co.jp use a different account system, with .com and .co.uk you can login with your existing email address and password)
here are 4 pictures i just made that should help you do what you want
http://postimg.org/gallery/bk7cyacg/8839fa1c/
if you need any other help i'll help you out more if you want.
if you do not have an address that you can use for the american address, just pick something simple like a hotel, find one on google etc, like 'florida hotel'.
for the payment, your card should already be on the account, and it should work just the same as from the uk.
-edit. i'm not sure for ebook purchases, but when using your 'foreign' card on the other store, usually amazon gives you the option to pay for the item in your own currency, as in, you will not get 'hit' by your bank with a $2, £2, whatever, foreign transaction fee. but kindle purchases use 1 click ordering right... so you might not see that screen? either way, nothing at all to worry about in the slightest