When defining a material's conductivity, we usually consider its conductivity of heat and conductivity of electricity separately. However, I realize that materials like metal conduct both heat and electricity well. In contrast, materials like wood and glass conduct both heat and electricity poorly. Therefore can we conclude that if a material is bad at conducting one kind of "flow of energy", then it will also be bad at conducting another kind of "flow of energy"? Thanks a lot.
The ratio of thermal conductivity to electric conductivity is a constant at a given temperature. This relation is mathematically defined by the Wiedmann-Franz law.
There are exceptions to this. The human body is a bad conductor of heat but is an excellent conductor of electrical.
Diamond is a good thermal conductor but a poor electrical conductor.
As an Engineer I can assure you that many electronic devices work just because there are materials that are good thermal conductors but excellent insulators as well.
Electronic device and equipment, especially those designed for high power, must get rid of the excess heat produced by electrical power dissipation. Most of the time because of joule effect, but there are other dissipative phenomena like the reorientation of magnetic domains in a ferro-/ferri-magnetic materials (e.g., transformers core).
Not being able to get rid of that heat will cause the device to fail because of its temperature rising above its safe maximum.
The use of electrically-insulating thermal conductors allow to improve thermal conduction inside a device/piece of equipment without causing short circuits between parts placed close together.
A classic example, used even at the dawn of electronics, is mica (Wikipedia article). Excerpts (emphasis mine):
Sheet mica is used principally in the electronic and electrical industries. Its usefulness in these applications is derived from its unique electrical and thermal properties and its mechanical properties, which allow it to be cut, punched, stamped, and machined to close tolerances. Specifically, mica is unusual in that it is a good electrical insulator at the same time as being a good thermal conductor.
Water is an excellent thermal conductor but a poor electrical conductor.