This Destiny: The Taken King guides provides detail on where to find Key of Gnashing Teeth chest location and how to unlock it with key. This Gnashing Teeth Chest is located in the Hall of Souls. The exact place is under the summoning platform in front of the Court of Oryx. The advise i can give here is to loot the chest when you are at this place with a few other buddies, and by making use of statues and starting the event.
Now here is the tip on how to get to the Key of Gnashing Teeth chest. It steps are similar like the most other keys. You have to use Wormfeeder rune and killing 50 enemies without dying. Now to get this Wormfeeder rune, you first need to have Wormsinger rune. Once you get it you will e rewarded with a random key. If this random key doesn't work out to unlock Gnashing Teeth Chest then repeat the entire process again.
The alternate way to get the key is to wait for it to randomly drop during Patrol. Watch the video guide below for more details.