If you have either an Amazon Fire TV Stick 4K or Fire TV cube (prev generations aren't 4k compatible only 1080p/720p etc), and it's not playing your favorites videos in glorious detail-rich 4K then you can check and test these settings first.

Another important factor to consider is your internet connection, for most people, this isn't an issue but it can also cause buffering or stuttering problems with 4K HD content and if the video supports 4K e.g. youtube example it may not display it straight away or not at all because of the aforementioned. Wireless interference can also be the culprit so plugging your devices into a wired connection is great for testing.