My flatmate has a girlfriend and I am angry at her.
How has she made you angry?
I don't know. She has a lot of issues, and I'm tired of listening to her problems.
It can certainly be difficult to get along with a friend's partner sometimes, but you should try not to get angry with them. If you start an argument with your roommate's girlfriend, it will make your living situation awkward.
I'm thinking about breaking up with my flatmate, so that we aren't roommates.
You should not start an argument with your roommate's girlfriend, but moving out seems like an extreme solution to this issue. You should have a calm conversation about the issues you are having. You don't have to like their girlfriend, but you can learn to coexist peacefully.