As a starter for where to look, and what to look for, this has been covered many times.
The principle of the rocket heater is that you burn fuel at high temperature for as long as possible. To get the temperature, you need not to lose heat from the flame, hence the insulation. Now here's the clever, and important bit, when the gases get to the barrel having been got as hot as possible, and having got up the riser driven by the heat, they get cooled by contact with the barrel. As they lose heat and fall in temperature, they drop down the barrel. This is the other half of the heat pump. The heat riser, does what it says on the tin, and makes the gases rise. The barrel cools them and makes them fall down the outside of the riser. This is the power that drives the gases out of the flue.
So that you can have hot gases in the riser, and cooler gases (they will still give you a nasty burn) round the outside, you need (you've guessed it) insulation.
This is in Ianto Evan's book and in several places on this and other forums. Understanding this principle and understanding the need for a huge exit hole from the barrel to the flue are the two bits of knowledge without which a
rocket stove will fail to perform.
The burn chamber needs insulation to allow the gases to stay as hot as possible. The burn chamber
should stay as cool as possible on the outside, so the heat stays inside, achieved by insulating. The barrel is the first point where you extract heat, followed by the flue, where massive heat sinking is needed rather than for insulating.