This is a piece of pipe, generally made of perforated sheet, which is inserted inside the exhaust system where the hottest gas is found e.g. right where it joins onto the cylinder.
What is the reason for these?
From what I have read they can cause a lot of trouble, because they tend to disintegrate and a piece can come off and block off the exhaust for one or more cylinders.
My understanding is like on chainsaws, the idea is to not allow much in the way of flames to get out and potentially cause a fire. Maybe light oil / fuel.
I believe in the US you can get your exhaust repaired and the flame cones disappear.
These perforated pipes are just a ridiculous attempt for minimal silencing on private aircraft. Flames are no factor basically, see the video in my link – and enjoy :
Super Constellation night takeoff:
If the material was a solid sheet then it might be to protect the initial part of the exhaust system.
In the Bonanza, the flame cones are located aft of the muffler in the tail pipe that extends out of the muffler. Their use is to reduce noise and increase the heat transfer in the heat exchanger. You can inspect the by shining a flash light up the tail pipes.
