Kawasaki disease is not a contagious disease like some other diseases so since Kawasaki disease is not contagious an adult or anyone else near the child who has Kawasaki disease cannot catch it themselves.
So while adults can get Kawasaki disease you cannot catch the Kawasaki disease from your child or anyone else's child or anyone who has it.
The Kawasaki disease can be passed down through genes though through family so if someone else in your family had Kawasaki disease then the child may get it.
It's possible for adults to get Kawasaki disease but it's also very rare that they do.
The Kawasaki disease is most common in children and causes symptoms such as acute vasculitis, mucosal inflammation, rash, cervical adenopathy, hand and foot swelling, and late fingertip desquamation.
Most cases of Kawasaki disease are not very serious in otherwise healthy children and adults but if the child or adult has heart conditions or artery conditions then the Kawasaki disease can sometimes be fatal even with treatment.