My four year old for stomach flu, vomiting and diarrhea, it's going around. Can I give him promethazine or loperamide?

Maybe. Those meds could be used in a child that age but not without speaking to a medical provider first to confirm the necessity and the correct dose. In many cases of stomach flu all that is needed is to maintain fluid balance using the proper replacement fluids. Often all that is needed is water but larger volumes of loss may require electrolyte replacement. Know and look for signs of dehydration.