I am going to assume the school you are looking at is Avery Coonley. That is the only school we didn't look at as it was too far south for us.
That being said, I think they all follow the state guidelines for kindergarten entrance and that silly September 1st cut date. Our local district does have an early entrance to first grade but NOT to kindergarten. To be eligible, the child must complete a kindergarten program with a certified teacher and have attended that same school for preschool. The child must also score in the 90th percentile on spring MAP as if he were in kindergarten (ds just missed the reading at 87th percentile and was 99th percentile in math) so he didn't skip kinder!
Not sure if this helps.. the other schools in the burbs are DaVinci (Elgin), Einstein Academy (Elgin) and Quest (Palatine).