How does this microwave kiln achieve such good insulation?

Microwave kilns are made of a white insulating material. It is generally composed of a porous ceramic body with an inside coating of high temperature susceptor material. A susceptor material is the one which absorb microwave energy. Some of these can reach temperatures upto 1000 degree celcius. The actual composition of these materials are not known since they are patented trade secrets. The insulation of the kiln is the main reason of it reaching high temperature. The susceptor material to plays an important role.

The high temperature is achieved as in any kiln, by good insulation. The temperature in any oven or kiln depends on the balance between the heat input and the heat lost through the walls. With perfect insulation you could achieve any temperature with almost zero power. In reality as the temperature inside increases the heat flux through walls increases and eventually it becomes equal to the heat input. In this specific kiln the only thing that is different is the way you input heat inside the kiln. Rather than using ohmic heating or gas burning (or any other fuel) you use the microwaves. As I understand it, the microwaves are not heating directly your "material" as they do in the kitchen ovens but they heat some special absorbing layer. Other than that, the "mechanism" of achieving high temperature is the same as in any oven.