The Fire TV 2 running software version 184.108.40.206 is rootable through two methods.
Method 1: KingRoot with a PC
This method is the ideal method for most people because it does not require having an A-to-A USB cable.
- Root using KingRoot. Try using the latest version of KingRoot, but if that doesn’t work, then find version 4.9.6 or 5.0.1 because those definitely work.
- Install TWRP custom recovery using this guide.
- Install the latest pre-rooted ROM using this guide.