Our public school district is considered very, very good, top 5-10% of California. They don't push reading heavily in kindergarten but do in first grade.
Out here, at the start of first grade, 50% of the kids can't read much (although they have excellent pre-reading skills like phonics, etc), 50% can read. However, the non-readers quickly get up to speed and are reading by the first few months of first grade. And they take off afterwards.
1/3 of the second graders in our school read either 400 books or chapters in books at or above grade level in 4 months, in the school reading contest.
Magic Tree House is a great series and it's labelled as third grade level.
I think reading for kids really blasts off around second grade.