I use this device from Monoprice to transmit to two Bluetooth devices while flying: https://www.monoprice.com/product?p_id=9722
It is kind of tricky to get set up but works quite well assuming you will be using the same headphones all the time (pairing/re-pairing the headphones is the trickiest part).
My wife and I had the idea to watch TV using two sets of headphones while our baby slept, so I tried to do something similar recently, without any luck. I have not tried with Bluetooth, but the Shield TV has 3.5mm headphone ports on both the remote and the game controller. Sadly, only one works at a time. Hopefully the limitation is in the Shield Devices drivers and not a kernel limitation that permits only one audio output.