Did you sign up on Amazon Japan with your regular Amazon US (or whatever your local Amazon is) account?
If yes, don’t do that. Create a new one. You can’t share content from Amazon JP account to a US (or your local) Amazon account anyway.
If no, then when you are asked for you address, just put any Japanese address in. Any address seems to work if it is Japanese. Use Nintendo’s address if you want! As long as the address you input was the Japanese address first, you don’t need to mess around with changing regions, etc.
Once you have a new account, add your credit card and your local address so the CC doesn’t decline.
You can absolutely buy Kindle content with a Japanese address using a foreign credit card. You can’t, however, purchase digital music this way for… well, who knows.
Once you have the content, you can either convert your Kindle reader to the new account or do what I do. Use your iPhone/Android/Computer with the Kindle app. I like this option as you can easily create flashcards, etc this way.