How many kilo calories does 1 gram of fat supply?

The answer depends on the TYPE of fat, in more ways than one.

If you burn fat, the chemical composition determines how much energy is released.

If you EAT fat, well its a different matter to an extent because we simply CANNOT process some fats, so that they offer us no nutritional value (and nutritional value is, of course, a type of energy). One example of this is Olestra (trademark name).