Here is another video from Krazy Kooks In The Desert 2006 er I mean Burningman. There was a similar video from 2005 however in that video the fire jet just hung off a pole on a single rope. They upgraded it a bit since then and this time it is a pendulum with the fire jet swinging around up in the air on a pole. It looks like there are five burners, one up, one towards the camera, and one on either side. It seems like it is RC controlled as they shoot one side burner to swing it one way and then shoot the other side burner to swing it the other way. However the pendulum weight is also giving it some movement. It's basically a jet engine on a pendulum swinging around.
Check out the video of the fire pendulum below or click over and view it on the host site.