Cinavia is transferred within the audio track despite which container you choose to convert the source into (.mp4, .mkv, etc.). Whether or not the protection kicks in depends on the type of player.
The Cinavia protection will still exist inside the audio stream; however, given that the Kindle is not a Blu-ray 'disc' player I'd go out on a limb and say you shouldn't run into Cinavia using it as a playback device.
