My son had a flat. Then he drove it awhile.
Then he and a friend tried to fix it. They didn’t set the parking brake and it fell–twice. Is falling off the jack likely to have caused significant damage?
Car damage is least of your problems.
Significant damage to the car or the person the car lands on?
You’ve got the right heading for the post. Get the kids AAA road service. The jack falling could cause very severe damage, it depends on what the jack landed on.
If it was just once, I would say it isn’t likely. Since it was twice, and he drive on a flat, this car should go in for a check-up.
Idiotic? Maybe, but I doubt it.
Inexperienced? Definitely.
What the lad needs is a couple of basic safety, auto repair and care courses.
I would think sooner than later would be prudent.
He was lucky this time. If it happens again …
The 1949 and 1952 Dodges that my parents owned came equipped with a wedge and the owner’s manuals told the owner to chock the wheel that wsa diagonally opposite the tire being changed. Even though modern cars don’t have bumper jacks, I still use a wood block under a wheel when I jack up a car. As to whether or not the car was damaged, I would have a shop put it up on a lift and a mechanic take a look.
I believe what is damaged the most and needs the most repair attention is your relationship with your son. The heading speaks very loud and even if the kids mess up big time name calling like this does more damage than a bent rim. It cuts to the core.
I agree with Roadrunner; they’re not idiots, just inexperienced.
Just my opinion, but the jacks (word used loosely) that modern vehicles are outfitted with are a card-carrying curse to the nth degree. Small pads underneath, dinky jacks with a small footprint, and it’s an accident waiting to happen even on level concrete. Mix in a dirt roadside or slanted shoulder and the odds of trouble increase even more.
What should be done is that every vehicle should be fitted with a jack like the old VW Beetles were equipped with. Small, lightweight, and it simply plugged into a square hole on the side of the car. Also useable in the dark with no problem. Both wheels on the same side would be raised and the jack could not turn nor could the car roll off of the jack.
Of course, that would hurt styling and that always comes before function. 
If the vehicle fell on sand or soft dirt, there is probably no damage. On concrete or blacktop, possibly but not inevitable if all of the wheels were on the vehicle. I’d be most concerned with the wheel with the flat tire, no cushioning there.
Before I would let my kids use any of our cars I instructed them on how to use the jack and change a flat…and some other basic mechanical knowledge which I believe everyone should have who drives a car. AAA isn’t a bad idea…but I’d prefer they know how to do the simple things first. You could wait for HOURS for a tow-truck or AAA.
You can’t expect ANYONE to automatically know how to safely change a tire…Before you hand the keys to the kids, you need to educate them so you won’t have to use terms like “idiot”.
The car fell? Why did it fall? Ans.: There is not a jack stand in the car with which they could have safely supported the car once they got it raised with the piece of junk jack which the car maker supplied with the car.
Remedy: Go to auto parts store and buy a decent hydraulic jack and jack stands. Hold class to instruct in use thereof (Include actual tire change).