I'm willing to deep dive this issue with whoever is up to it. The Plex app is literally useless on Samsung - I'd have to turn the quality practically all the way down to get it to work to where it's unwatchable.
I can start a movie on Samsung with it buffering all over the place and then stop and go to the bedroom TV and start Plex on the FireTV and it works flawlessly. Plex also works on...all phones in my home, all laptops, all desktops but the one I'd most rather have it on is the big, nice TV.
Let me know what kind of information I can provide on my end. Packet logging, Plex server/client logs, etc.
TV: Samsung UN55KU6290 version1206.1 // WIRED connection
Home internet: Gigabit
App: Samsung PLEX app
Server: Dual Xeon E5-2699 v3 / 384 GiB DD4 RAM / 40Gbps burstable, 1Gbps sustainable
Server Plex version: 126.96.36.19925