I have this exact issue too. I can play a file through direct play over Emby without any issue but if I try to play that exact same file with Plex, it detects a much slower internet connection than I actually have and buffers / lowers the quality.
I’ve tested the connection of my Fire Stick and I get consistent high speeds. Emby on the Fire Stick can make use of those speeds but Plex on the same stick can’t.
May need to see logs but while something is playing check the dash board in the web app and see if it shows the IP of your Fire device as remote, local or indirect.
In the settings of the app in the Video Quality row make sure Home streaming is set to Maximum and in the same group of settings possibly disable Quality Suggestions which does a check on speed it might be getting wrong.