The truth is that this is a difficult situation with no easy answer.
From the legal standpoint (depending on where you live), you may not have the choice: some actions (like hitting in the face) are considered child abuse and you are legally binded to report it if you see it happening. But if your goal is to help that family, then that option is not really a solution, because the resulting trauma for the child can be worst than the initial problem.
Intervening in somebody else's parenting habits is always delicate. You are going to meet resistance, and the more you push, the more resistance you will get.
Most parents who use spanking and yelling do so because this is how they themselves have been parented; they had to internalize and "justify" their own childhood suffering in order to cope with it. So when you tell them that they could do things differentely, you are challenging them to revise their own childhood, to accept they may have been hit for nothing by their own parents. In addition, accepting the idea that spanking can be damaging means that they have to come to term with the idea that they have been damaging their children all these years before. This is hard! The guilt can be so powerful that the mind may simpy resist and go into denial - no matter the arguments or proof you give - because acceptance is just psychologically distressing.
I found these 3 attitudes can really help:
1) Speak in "I" about yourself; how it makes you feel when you witness something, how it breaks your heart, how you feel uneasy, etc. Do not put blame. Do not accuse. Do not say "you...". Speak in "I". Show your vulnerability rather than attack his choices or behavior. And NEVER stop yourself from being authentic and honest IN THE MOMENT. So if you witness something.. don't stay there in shocked silence. Be real - not angry, but show you are shocked. Be authentic and vulnerable.
Exemple:
Brother: SLAP!
You: "Ouch. I hate it when I see this punishment going.. it breaks my heart. I feel terrible looking at this. I feel as if I was the one who got slapped."
2) Listen to the parent's justifications or explenation, the "why" they do it. Find the core, the desire to help the child grow, the fear that they may not have learn something that the parent thinks is needed to learn for their own good, etc. Then voice it back, name the fear, name the emotion. Show you undestand and agree.
Brother: "Sorry you had to see this, but he has to listen to me when I talk. It's unacceptable that I get ignored."
You: "You don't like to be ignored. It gets on your nerves?"
Brother: "Yes it does. He doesn't respect me."
You: "It seems important for you to get that respect from your son. Do you feel like sometimes you are loosing that respect?"
As you progress toward the "why" of the behavior you may gently open the door to a conversation on alternatives - because now he feels his needs are understood.
3) Next time, show, don't tell. It's much more effective to demonstrate a different way of doing things than to lecture someone about it.
Next time, when you see your brother about to get angry because his son isn't listening, step in:
Kneel down at the kid's height. Lock eyes. Gently grap his shoulder with a hand. Smile. Say "Hey buddy. I know you are having a great time right now, and you don't feel like stopping... but daddy just spoke to you. Let's hear what he wants together okay?"
If he can see how effective this is first hand, it's the best way to get him to actually ask for advices.
This is all assuming that your brother is rough, but not abusive.
I am not convinced of that, from your posts, but with no additional context, it's hard to say for now. It could be that you are only seeing the tip of the iceberg and that things are much worst in private. If that's the case, then it's no longer about teaching better parenting ways, it may be a case for reporting abuse or anger management.
Hope this helps a little!Nicolas, Family Life Educator