It usually is more inexpensive to fly with the chinchillas(than sending them on their own.). As far as I know, most airlines don't allow carry on - the chinchillas still go in the cargo hold. They will fly in the cargo on the same flight your son is on though and will be checked in as baggage. That is how the airlines do that here.
Usually what costs $100 (example) to fly a chinchilla on their own, only costs $40 to fly them as checked baggage with you on the flight. I know here, they do put the chinchillas on the luggage carousel though, if they are checked as baggage. I did the same thing with a couple chinchillas when flying from Calgary back home, once. Normally I would have paid like $100 for them, but I only paid $40 by checking them in as baggage.
I didn't even have to make any extra flight arrangements for them other than my usual flight arrangements for myself. That was through Air Canada, but I am sure most airlines are the same.