Think its wrong that I'm going to ask my flatmate why she slept with my friend?
Why are you going to ask her about sleeping with your friend?
She's been lying to me about other things, I want to know. I think her cruelness should have no space to exist.
I understand why your angry, it was rude of her to sleep with your friend. You are within your rights to interrogate her.
I'm going to put her on blast on social media and make her feel terrible.
You should talk to her in person and not online. That might cause a lot more trouble than its worth. It's better to talk to her face to face.