flip out on someone

"If you ask me a single question, I'm going to flip out on you."

Does it mean to get mad at a person?

Not necessarily mad, but definitely annoyed.

Hmm. I can't really agree with Sharon on this. When you flip out, you not only get angry, but you ACT angry - you yell, rant, rave, maybe even throw things. There are definitely actions associated with your emotional response.

Yup, "flip out" implies visibly and demonstrably angry.

Not teacher

It can mean to reach the breaking point.
If you keep poking that animal in its cage, it will flip out and attack you.