Most gifted children cannot get into kindergarten any earlier than other children unless their birthday falls within just a few months after the school year starts. For example: Your child will turn five years old in September but the school year started the first of August. Then, usually the school district will allow that child to go ahead and start kindergarten. Now your child can attend a gifted preschool program if he or she cannot attend kindergarten just yet. You need to check with the school that your child will be attending and see if they offer a preschool program for gifted children. A lot of schools do and most people do not know that so check around and see.
My child has a November birthday. He began Kindergarten (at age 4) at a small private school that he had previously attended. Our local public school has also been helpful in his on going education as an "early entry" student.