Why is glass a good conductor of heat?

There are at least two mechanism of thermal conductivity - free electrons and thermal phonons. The first mechanism can be prevalent in metals, the second one is important in dielectrics. I did not look up thermal conductivity of glass, but such excellent dielectric as diamond has higher thermal conductivity than any metal, as far as I know.

Glass is a very poor heat conductor. It has one of the lowest possible heat conduction a solid (without air trapped in it) can possibly have, this is mostly due to its lack of ordered crystal structure. Since it's an insulator, the electronic contribution to the thermal conductivity is very small. However phonons can still carry heat, but unlike diamond which has a well ordered crystal structure, glass lacks such a structure. This favors anharmonic processes, i.e. phonon-phonon interactions such as umklapp processes which severely limit the thermal conductivity. See this reference for instance.

One of the ultimate goals of finding good thermoelectric materials, is to achieve a glass-like thermal conductivity. In that case the thermal conductivity needs to be as small as possible. Here are some references.