In case you haven’t noticed, your Kindle Fire HDX does not have a HDMI port anymore. That means you can’t connect it to your TV with a HDMI cable. That’s not necessarily bad. These 2 wireless display adapters for Miracast devices let you watch your Amazon content on your TV without needing a HDMI port on your Kindle:
NETGEAR Push2TV Miracast HDMI Adapter: this device is certified for use with Kindle Fire HDX. It wirelessly displays content in up to 1080p HD resolution. The device is very compact.
WiFi Display Dongle: a generic dongle that works with Miracast devices. Just plug it into your TV’s HDMI put, and you are ready to go.
I still prefer using my old Kindle that had a HDMI out for doing presentations. But if you want to do it wirelessly, the above products give you that option.