This phrase refers to a certain rude gesture. In the United States, it's quite rude o do this:
- face the back of your hand toward someone
- stick up your middle finger
- lower all the other fingers on your hand
Doing this toward someone is called "flipping them off".
The object of the phrase "flip off" can come in between the two words, or after them:
He got suspended for flipping the bus driver off.