Hand 'em a bagel and keep one in your own mouth when they run the postmortems. Cheap kiddie kits and lightweight specials with nothing but plastic pseudo scissors, pins, and Band-Aids are dangerously useless. Stage a camp disaster and teach your kids the whys of pressure and elevation, immobilization, sterile covers, and the recovery position. Help them figure out triangle bandaging, splinting, and pulse rates. Setting up a bush hospital can be a blast for kids.
First aid is never a game.
Back in camp, the possibilities are manifold. There are routine chores and the tribal stuff. Kids can collect kindling, drag in wood, and saw it. They need to create, control, use, and put out a fire. Teach them to build a one-match fire and to boil water in a metal cup, on coals, to make it potable in unsafe water areas.