Readability sends articles to your Kindle device as Personal Documents by way of the email address Amazon provides for each device. These include Kindle Keyboard, Kindle, Kindle Touch, Kindle Fire, and Kindle Paperwhite.
Readability articles and digests also appear in the most recent version of the Kindle app for iOS. (Choose an @kindle.com email address for your device in the app or on Amazon's site)
You can read more about Personal Documents at http://www.amazon.com/gp/help/customer/display.html?nodeId=200505520
You can edit the email address(es) of your Kindle(s) at https://www.amazon.com/gp/digital/fiona/manage?ie=UTF8&ref_=kinw_myk_surl_2&#pdocSettings