It's not going to work on several fronts.
1) Your circuit is probably overloaded, even if "everything else is off". If you have a 100A Main, you cannot really load it to 100A (unless someone specifically ordered a 100% rated breaker, very rare). Standard breakers can only be loaded to 80% continuously. Assuming the service is 230V 3 phase, you already have 48A from the big motor, 10A from the smaller one, which leaves you only 22A for lights, outlets, air conditioning etc. I seriously doubt you can work in the dark and heat, plus I would assume a dyno has other associated loads, i.e. a computer of some sort, some instrumentation, a printer etc. Maybe you'll get lucky though.
2) The starting current is more likely to be 6 times the FLC, so in this case 288A for the large motor, but that is somewhat irrelevant anyway. Although a typical 100A 3 phase thermal-mag main breaker is going to have magnetic trips factory set for 400% of rated current (400A in this case) and therefore probably capable of holding in during a fast startup, keep in mind that when you go to energize that big motor there will almost surely be a severe voltage drop, even with nothing else on. That will cause a severe drop in starting torque and unless your control system has some method of unloading that motor, it may not accelerate to full speed. The typical "rule-of-thumb" for circuit capacity sizing to avoid a voltage drop of more than 5% when starting a motor across the line is 2.5 - 3 times the motor HP as kVA, so for that 10HP motor that means 25kVA minimum. On a 100A 3 phase 230V service you theoretically have 40kVA available, but in this case the motor is 1 phase so not all of the 3 phase kVA is available to you. You really only have 23kVA available for starting power. Were it a 3 phase motor I might say go for it, or put on a soft starter. But 1 phase motors can't have soft starters applied to them (some can, but not cap-start as this almost surely is), plus if you don't accelerate to 90% speed, the start switch never opens to take the caps off-line, so the motor never can finish accelerating. Even if you get lucky again and it does manage to accelerate, it will undoubtedly take longer and probably trip the thermal trip elements of the breaker anyway.
3) As to breaker sizing, you are correct about the MAXIMUM breaker size being 120A, but breakers don't come in that size, plus don't forget you have a 100A main ahead of it, so you will have to settle for a 100A anyway. It might still hold in for starting though, with the provisos I laid out above.
It could possibly work if he changes to 3 phase motors however. What I would do is change them now because I am convinced it won't work, but if he wants to be cheap, try it with 1 phase and see if he gets lucky. The worst case; he smokes the motors and has to replace them, then replace them with 3 phase. To keep the installation cost risk lower, size a 3 phase motor starter for the 1 phase current and use 2 of the 3 poles for the 1 phase trial. If it doesn't work and you have to go to 3 phase, you don't have to toss the motor starter and re-install, all you will need to do is change the overloads. If you buy some types of solid state OL relays, you won't even have to do that, just dial it down. Do the same for the motor leads, run all 3 but only use 2, sized for the 1 phase service, then they are just a little over sized if you go for 3 phase but you don't have to re-pull them. You will need to swap out the breaker though. You will need a 60A 3P breaker for the 3 phase starter.
Just keep the fire extinguisher handy at startup for those motors!
