My son went on a mission trip and is covered with heat blisters that are healing, could he get cancer from this much exposure?

Not likely: Most types of skin cancer are related to continued over exposure over a long period of time which is why you tend to see the majority of skin cancers after the third decade of life. These are the types that tend to appear on sun exposed areas. There may be some increased incidence in those with one or two significant exposures when younger but not enough to lose sleep. Just check skin regularly