There are multiple sites around the web stating that the Amazon Appstore is now rolling out worldwide however, Amazon themselves have not confirmed it yet.
I have just downloaded the app, was able to sign in and start downloading. I'm from the UK for those wondering. I can't see why it wouldn't work for other countries.
Download it, try it and leave your country in the comments so we can confirm the countries which it is working in.
You can enter this link into your phone to get direct download - http://www.amazon.com/app-email
or scan this QR code
Let me know if it works for you guys!