I have a Kindle Fire HDX, 3rd generation and the compatability section of the Muse website says the program is compatible with that device. An app search for Muse does not bring up the app. Search for “calm” and you will see the “Muse: the brain sensing headband” app.
Were you able to find it? The Muse app is available on the Amazon app store (http://www.amazon.com/Muse-the-brain-sensing-headband/dp/B00LGYXLZA). It is no longer called Calm, as you noted.
Yes I was able to find it when I searched for “Calm”. The Muse app came up next to Calm as a suggested app but I did not find the Muse app with a direct search of the word Muse.