If you are in an area where a jacket is always going to be worn at recess, then I think you put some basic items (gauze, band-aids, whistle, bandana, your business card with all phone numbers on it, flashlight, money) in a jacket pocket. The problem comes if you live in an area where jackets normally aren't worn. Getting children to keep tabs on EDC gear is like herding cats. At 7, your son just won't be able to do it with any regularity and the pockets on the pants of 7 year old boys just aren't big enough to carry much.

Moreover, a first aid kit isn't really something your son needs to carry around at school (ok, I'm being something of a hypocrite here, as my son's backback includes minimal first aid supplies). The school has a much more complete first aid kit than your son will be able to carry in his pockets. And, if your son's first aid needs cannot wait the additional 5 minutes it takes to alert a teacher and get the first aid kit, then the injury will be so severe that a minimal first aid kit wouldn't cut the mustard anyway.

Very sorry to hear about the bullying problem. My own experiences never went beyond intimidation. Even big kids can be the targets of bullies, since bullies have no compunction about acting in packs. My 7 year-old son is small for his age, but luckily is in a relatively small school and has not reported any bullying problems. Glad to hear that he will be moved to a smaller school.