Our school is moving toward team teaching. Last year, he split time between two teachers. This year, it's between four. So in our case, asking for a specific teacher would not have worked.
When he was in Kinder, I did ask for a meeting with his teacher at year-end (she encouraged parents to meet with her for an end of the year wrap up so you would know what to focus on over the summer --- loved her!) I asked her then if she knew which teacher he might get. She told me they hadn't made their recommendations yet at that time. We discussed his personality, ability/willingness to listen/follow directions, etc. and I asked her to *please* consider the teachers' personalities and recommend whichever she felt would handle him and his needs the best. We had a great experience with his first grade teacher, so I think she chose pretty well.
Maybe that's a way to approach the teacher? Perhaps not outright ask, but lead them to the water you want them to drink by showing how your son and the teacher of your choice are a great match.