Jailbreaking/rooting is not necessary to get Kodi on your Fire Stick. You can manually download the APK from Kodi's site and sideload it from within either Silk or Firefox on the device.
Overall, the AppleTV is going to be a much nicer experience (Amazon devices are constantly presented ads for things you don't care about), but they are also 4 times the cost or more. The Fire TV Stick 4K is the best deal/bargain for a Channels client. The AppleTV 4K is the best device for a clean/distraction free experience ... but also more expensive.
(The AppleTV was the primary development target of Channels, and tends to get the most attention from the developers, too.)