Joe got an Amazon Fire TV, but when he plugs it into his Denon AV receiver it doesn't work. Leo says he likes the Denon AV receiver and can't imagine why it wouldn't work. Everything in the chain is "HDCP" complaint for copy protection. So it should work just fine.
Leo thinks it may be a bad port or bad cable. Make sure the settings from the Fire TV and the TV itself are matched. If one is 1080i and the other is 1080p, then the handshake could fail. Turn everything off and unplug it. Then plug each thing in one at a time, ending with the TV.