If you're used to wrenching on cars, this ought to be a piece of cake. There's no OBDII diags or anything, but the troubleshooting logic really isn't too much different whether we're talking cars or bicycles: Identify the problem, diagnose the cause, then address that root cause. In this case, we still haven't gotten past step 1. The problem's apparent -- we know you're getting flats -- but we need to diagnose the cause in order to come up with an appropriate fix. The fix may be "mainly composed of you ordering something", as you put it, but the trick is to figure out what that something is.

There should already be a rim strip of some sort in place to prevent the tube from getting punctured by spokes, and/or spoke nipples. (Or spoke holes if you've got a double wall rim, which probably isn't the case on a kids' bike unless it's pretty high-end.) If your existing rim strip is in decent shape and covers everything it's supposed to, there's no need to replace it.



Higher pressure is only going to help you prevent flats if your flats were being caused by insufficient pressure in the first place. If underinflation isn't the cause of the problem, going to higher pressures isn't going to fix it.

The location of the hole(s) in your flat tubes will probably tell you what you need to know. Find the hole and proceed from there. If the hole is on the tread side of the tube, you may have a sharp object embedded in the tire that punctures the tube when your son's weight pushes it through the tire rubber. If the hole is on the rim side, you may have a problem with your rim strip and the tube could be getting punctured by a spoke or something. Or maybe a burr or rough weld. If you've got "snake bites", then let's talk about air pressure.