Frustratingly, you can't get the kindle version if you live in the UK (I actually live in the Netherlands, which Amazon doesn't operate in at all, but my account is from the UK). The kindle version even shows up on the US site until I log in.
EDIT: I tried to use Amazon.nl (they do have a kindle store, just not regular Amazon), they have the kindle version of the book but when I log in after buying it I'm told it's not available in my country
It seems you solved the problem, but for the next time: You can add a U.S. address in your Amazon account (any random address will do) and set it as the primary address. Then buy the book, and right after switch the account back to your real address. I think I have even seen Amazon recommend this solution.
EDIT: I tried to use Amazon.nl (they do have a kindle store, just not regular Amazon), they have the kindle version of the book but when I log in after buying it I'm told it's not available in my country