The full version of the Calm app is not currently available on Kindle or Amazon devices. Amazon devices only allow updates from the Amazon store which unfortunately does not have the version of the app which supports subscriptions. While we do hope to have the version in the Amazon store eventually, at this time the subscription version is only available for Amazon devices that can download apps from the Google Play store.
That said, you may be able to access the meditations through your tablet's mobile browser. We recommend trying to open www.calm.com/meditate and see if you are able to log in and access the meditations there. The site is not optimized for this, but some users have been able to successfully use their tablet browser for meditations.