We just got a trampoline and the first day my 12 yr old son was fine. Jumped for about an hour. Then on the second day (the next day) his chest hurt.?

Hopefully okay. Chest pain in children should be approached with caution, may be he over do it and minor bruise in the chest cage, if continue i advice you to check it out.
Splints! Mild diaphragmatic irritation is common after a first bout of aerobic exercise. Both the liver and spleen can rub the diaphragm and have a temporary inflammatory response. This will dissipate with time. It should respond to nsaids. If the problem persists and does not improve, see your doctor!