What treatments for kawasaki disease can I try at home?

None. Kawasaki disease is a serious illness and you should consult an md asap.
Kawasaki disease. Since the diagnosis of kawasaki disease is usually made in conjuction with hospital admission for children, it would be very unusual these days not to be treated in the hospital with intra venous medication. Other than the occassional use of Aspirin when indicated specifically by your cardiologist there are no known home remedies or prevention.