I'd be wary about assuming that a child who had finished a private kindergarten would be moved quickly into first grade. Schools can be very skeptical about this kind of thing. For example, my eldest was offered a skip to fourth grade at a private school, but we had been thinking about moving him. The public schools in our area all said no to a skip, except for one, which said, "Well, we can put him in 3rd grade for at least 6 weeks and then decide." This was their way of saying no. Moving after 6 weeks would have been too disruptive for him as a new student, and they knew it.
Not all schools are so narrow-minded about acceleration, so my advice would be to call them and ask. Tell them something like, "Little Joey finished kindergarten at a private school, and he turns 6 in February. What's your policy about promotion to first grade?" If you don't like that answer, ask, "What if we kept him in private school for another year? What's about promotion to second grade?"
Some schools are wonderful and will try to work with you. Some have blanket NO ACCELERATION, EVER policies. Others are in between. My advice is to find out where your local principal fits on that spectrum and plan accordingly.
Here in MA, we know of a family with a bright girl having an autumn birthday who put her in private school for KG and 1st grade, intending to transition to public school for 2nd grade, as two of our children have done. When it was time for her to transfer, the principal strongly encouraged them to put her in 1st grade because the 2nd grade class sizes were getting too large! They agreed, and their daughter was bored in 1st grade. I guess the moral is not to take anything for granted when it comes to acceleration.
