Nope, no native app available (shame on Apple), no chromecast compatibility and no browser streaming under Android wich is really anoying and is preventing me from watching the shows (buying an Apple TV is not an option).
Well in fact there is already an ATV+ Android app wich is the Firestick one, I downloaded the apk, installed it in my Android TV but then it asked for a valid amazon app store account to check wether you have the right to use it. I managed to also download the amazon app, installed it, login into it but then the ATV+ app said I didn't own this app and stopped working.
So the fact is that an android app is already working but can only be used if you own a Firestick. Weird thing.