I've got a Kindle, and it does still work me -- I've just checked as I wanted to get today's New York Times. Note, however, that the Kindle was registered and used in the US by the friend who got it for me (so, as they say, your mileage may vary).
A couple of pointers from when I tried to get it working.
1) You must
not have a non-US credit card associated with the account. It checks this and will block any purchases using the account, based on the card. So when I first did this I had to remove the credit card from it.
2) I think it needs a valid US billing address, number, etc associated with it. (I changed this first before deleting card details).
This means I need to run a completely separate account from my normal Amazon account.
Although I need to go to the Amazon MediaLibrary to manually download the content (but I still got the issue of NYT in under two minutes.)
(I'm not sure I'm popular with my friend as a result of asking them to get the Kindle; whislt they had it, they became addicted and had to buy one themselves and now claim to have a
large book, magazine and newspaper bill as a consequence. Something I fully understand!
)