If it is determined that nothing serious is wrong with your pinball machine, I suggest that you have an electrician take a look at the wiring in your house. If you have an electrical problem of some type in your house wiring, it could cause more trouble than just flickering lights. That is, assuming you are not electrically inclined and able to investigate the problem yourself.

I think it could be a number of things that might cause the light to flicker. It is probably a loose connection somewhere. Over time, a loose connection will be build up carbon in the area where the wire is loose, which will get hot. The process will continue and can start a fire if it is left to get worse over time. Could also be an overloaded circuit or a voltage drop problem because of a long circuit on a wire that is too small for the load. Any one of these problems should be corrected before it becomes a major issue. Just my 2 cents...

I doubt seriously that there is a problem with the load capacity of your breaker panel. The real issue is much more likely a loose wire or an overloaded circuit. Most pinball machines will not pull enough current to effect any one 15 or 20 amp circuit breaker. However, if there are many other loads on one circuit, that the pinball machine is also connected to, that could be an issue. If you can do a megger test on the circuit that the pinball machine is on, a loose connection or other problem could be located. If you can't do that test or don't know what that is, that is what licensed electricians are for. One test that you could do, would be to turn off the breaker that runs your pinball machine and see what other major loads are turned off. If there are major loads on that circuit, you might try moving the machine to an outlet on a different circuit that is lightly loaded. Major loads would be things like an electric heater, HVAC, refrigerator, stove, electric water heater, etc, etc... If you do move it, make sure you use an extension cord of sufficient capacity, so that you don't make the problem worse. That is, of course, if there is not some other problem in the pinball machine that is causing your issue...