How should I try to get my older brother with Tourette's to quiet it down
Why do you want your brother to quiet it down?
Because I'm tired of listening to his endless complaints about me not being nice to him.
Your brother has a condition, tourettes, that he cannot control easily. Forcing him to "quiet down" is cruel and impositional and lacks understanding of his situation. Find compassion for your brother and treat him with patience.
Why should I put a good effort on this and help him? My brother is a mean bully.
I doubt that he intends to be a bully. With tourettes people sometimes say things that they don't really mean. Maybe when you feel overwhelmed by it you could try putting some space between you.