As many have already mentioned, there seems to be choppy playback when android media player is enabled on plex. Disabling that player renders the video smooth but with audio out of sync.
I am experiencing this on a one day old Fire HD 10 tablet with Fire OS 5.1.4
Both APK v4.26.1.653 and amazon v4.26.2.654 are experiencing the same symptoms.
I'll also confirm as others have, when I use an external player (VLC), no skipping or sync issues are noticed but the audio levels are reduced exponentially. I tested about 20 movies and shows, and I noticed that most.mp4 files had very little or no noticeable issues, while some .mkv files did display choppy playback and audio sync issues.