1. He is a Chinese teacher at primary school.
For this sentence, it is not specific, he could be at multiple schools. another example is " He is a student at school". the main focus of the sentence is he is a student.
2.He is a Chinese teacher in a primary school.
For this sentence, it is more clear that he is a teacher in only one school. The main focus is he is a Chinese teacher in a primary school, not secondary school, high school, or college.
3.He is a teacher who teaches Chinese in a primary school
This sentence can be written in a simplified way: He teaches Chinese in a primary school or He is a Chinese teacher in a primary school.
