It depends on what canon you want to follow. It also depends on what you mean by school.
What I mean by the latter is whether you mean normal school or Pokemon-specific school. Pokemon-specific schools have been seen in all kinds of canon, in the anime, the games, and the various manga. As for normal school, the type of school that we attend, that's up in the air.
Anime and game canon really don't say much on the idea of school, except for Pokemon-specific school. Ash and company visit a few Pokemon schools on the course of their adventure. Same in the game. The player visits a Pokemon school for trainers in a city, where want-to-be trainers go to learn battle moves.
I'm not really sure on Special canon, but I know that in the Electric Tales of Pikachu manga, Ash does go to school, probably a normal regular school. He goes on a short leave from school to go on his journey.
So, really, as was discussed in the Lounge, school is really up to the author's interpretation as to what to do because not much is known about it in canon. You can have the kids go to school until they turn ten, after which they could either leave for just the summer, or forever. And you can have any kind of schooling that you want, like if the courses are mainly about Pokemon for all the kids, or for only those kids who are interested in Pokemon, and even then those kids interested in battling, or contests, or just caring for the beasts.
But, yeah. It's up to you as to what to do because there's not much to really go on in the canons. Read up on the discussion concerning schools in the Fanfiction Lounge to see what other writers have done.
