This depends on which rule book we're following here, so you'll have to fill in that piece of information to get complete answer. I'm assuming by "kid" you're speaking of some level of play younger than college.
If you're playing by NFHS rules (most high schools), a kick is a kick until it is possessed. If it is muffed into the end zone (no possession), it's a kick into the end zone which is a touchback as soon as it enters the end zone (no possession required). If they had ruled that he had actually possessed the ball then fumbled, then the previous is irrelevant -- K can recover (and even advance) the fumble.
If you're playing by NCAA rules (Texas high schools, some private schools) or NFL rules (including semi-pro, which seems unlikely in this scenario), then K can recover the touched kick (but not advance), including in the end zone -- where it would be a touchdown.