Ex-Girlfriend question...?

Hello. I've been broken up from my girlfriend for exactly a week. I've been going out with her for two years, and it was inevitably me (It's complex) that ended it, as it was either I do it or her. She's been flirting with my friend; texting him infront of me, talking, etc. She sits across from me, and I have to endure him going up and talking to her- he says he only goes up to talk to other friends, but only seems to talk to her. I told him how I felt, and he said he had no intentions and wouldn't do it, yet however seems to continue. My ex-girlfriend still wants to remain friends with me, and I reluctantly said I still wanted to talk to her. I'm regretting it. How do I deal with my friend? How do I deal with the fact that she so hastily "got over" me, and is already flirting?