All lights flicker when running

I've never seen AC do this but I guess it could. So far as testing, all you need is a multimeter, and EVERY car owner who does their own work should HAVE one. Simply put the meter on AC volts while the car is running / charging, and check the alternator output stud. This will give you the ripple voltage. I don't remember what the "accepted" published limit is, but it will be WAY below 1/2 volt AC

assets.fluke.com/appnotes/automotive/beatbook.pdf