I have a six year old old grandnephew who when he gets mad screams at the top of his lungs and when he crys about something he somehow can move it up a couple of octaves. I want to smack him. I don't. I have tried ignoring it, threatened him and I've asked what is wrong? That makes it worse. Most of the time it is his fault for his brother's retaliations. This is a daily problem.
I have no experience with this but I'll try to give advice.
Screaming is a symptom of a concern, and you need to find out what it is. Punishing him may eventually get him to stop screaming, but it won't help because the anger will still build up and cause trouble later.
When he's not screaming, try asking him in a friendly way something like "Hey, what were you so mad about yesterday?" and try to work things out with him.
I could type a really long answer full of everything psychology and parenting experts would say, but what it boils down to is: this child is in need of a connection. He needs empathy and respect. He needs you to treat him like you would your best friend if she were hysterical about something. Be calm, gentle and supportive. Put words to his feelings, since he obviously can't. Let him know you're here to talk when he needs. Children who feel like they haven't been given a voice will scream because they have no other way of expressing their feelings. It's the same reason babies cry - they can't talk, but they have needs and they need to get the attention of their caregivers. Older kids are just much louder.
I highly recommend checking out some parenting resources on positive parenting and focusing on how to empathize and communicate his feelings to him so that he can put words to his emotions. Overcommunication is the key with young children as they still don't have the tools they need to understand everything that happens to and around them.
I understand your concern.
Are the parents equally concerned?
I'd try whispering, redirection and praise for good behaviour.
Most children who do not know us well, are slightly afraid because they don't know what you'll do in the face of unwanted behaviours. I'd always fall back on: 1) support the parent. (I will assume they are perfectly good parents.) 2) talk in a quiet and calm voice. 3) remove anyone unnecessary to the situation from the area. 4) offer an alternative activity like dancing, singing, another toy, a walk...
If I understood right, the trigger for these screams has to do with sibling conflicts. A great book for understanding and working on sibling conflicts is Siblings Without Rivalry: How to Help Your Children Live Together So You Can Live Too by Faber and Mazlish.
I recommend watching the two children carefully, so you can intervene and model some more effective ways of dealing with sibling conflicts. Hopefully before the scream starts.
At your grand-nephew's age you may also establish a rule about screaming.