I believe the meaning of "freak out" is broader than the meaning of "flip out." "Freak out" can be used more when losing composure over something that makes you angry, nervous, anxious, drives you crazy, or makes you excited. Whereas "flip out" only conveys losing composure over something that makes you angry. So you can use both only when you want to say you are extremely angry or upset.

Just as Rox said. "Freaking out" is much broader. For example, you can say I was freaking out when I saw my favorite actor, movie star, singer etc. Or when I was freaking out when I saw that id broken my arm. When you say "I flipped out" it's saying that you are conveying anger in a situation. I flipped out when he pushed me. I flipped out when he got in my face etc. I hope this help.

In America, they can be used interchangeably. They may have more limited meanings in other English speaking countries. Here, I think it depends on where you are from (East coast, the South, etc.) which phrase you use.