The more you tell him to use an indoor voice, the more you look at him in the mirror, the more his siblings talk to him the more he will continue.
Our grandson does this regularly. If we even look at him he gets louder, if we remind him to use his indoor voice he gets louder, if his sister has enough and tells him to be quiet he gets louder.
Spanking him, time out, taking away toys, nothing works because the goal of the activity is to get a response. That response is everything to him.
So totally ignore him, do not look at him, do not shhh him, nothing. Talk to the other kids and tell them to ignore him too.
He may go ahead and do this for a while but he will eventually pass out from exhaustion.
It's called homeostasis. The body has a system that helps it recover after a high energy activity. That's why we fall asleep after good sex...lol.
Your son is using an enormous amount of his energy screaming and fighting. Once his body runs out he will simply pass out until his body is recovered.
If this does not happen I suggest you take him to the park and see that he runs, climbs, digs, any activity you can get him to do for at least an hour before he gets in the car to leave. Once he starts the tantrum it should be shorter due to him having already used an bunch of his stored energy.
Watch on travel days for foods containing red dye 40, excessive caffeine, and other foods that might trigger a tantrum. Sugar does not have any effect as proven through scientific study. Sugar actually should give a tiny tiny burst of energy then they drop to a low and fell sleepy. Caffeine and other additives in those foods do have an effect though.
So, on travel days, use up all his energy that you can. Let him have as big a tantrum as possible because the bigger it is the quicker he'll fall asleep. If he doesn't then of course something else might need to be done.