Are chewing gum good for reducing face fat?

Diet. To reduce weight (loose fat) you need to diet and burn calories (exercise). In essence, you will burn off more calories in a day than you take in. Chewing gum excessively can strain your TMJ and cause more harm than good. Think of your whole body being in balance, not just your face.
Facial fat? To my knowledge there is no way to target facial fat with any exercise. If you are overweight in general, diet and exercise will improve overall health and reduce excess fat. If you have a problem specific to your face alone, see a plastic surgeon for possible cosmetic options.