At our school, we aren't allowed to pick teachers, but we're allowed to provide additional information for the school to use in making the assignment. "My kid does best with X, Y, and Z," where X, Y, and Z are characteristics of only one teacher, is an effective way of getting the assignment you want.
In our case, we said "We want DD to have a teacher who wants a grade-skipped kid," and got a teacher who was a perfect match for her. (And is generally considered to be the "best" teacher in the grade.)
