Sounds as though your son is very bright and quite advanced, Marcie. Unfortunately (or fortunately) the decision about whether to skip kindergarten isn’t usually left up to the parents. The principal, the teachers and the official policies of your school district are also entered into the equation.
What I would do is make an appointment with the principal and go over all of this with him or her. Many districts now use simple checklists to help make such decisions. Others insist on referring the child for a formal evaluation by a psychologist. Others operate under guidelines that permit them almost no flexibility.
Whatever placement you can arrange for your son, your continuing role as his major “teacher” will be a critical one. I’d start thinking about breadth of achievement rather than further depth in the areas in which he already excels. In other words, don’t try to teach him to count to 1,000 or write a lot of new words. Instead, identify some of his major interests and help him develop those. Does he enjoy art? Is there some topic (vehicles, dinosaurs, birds, etc.) he is especially interested in? Children’s museums are idea factories for children such as your son. I hope you have one near you.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.