Boyfriend flirting with coworker?

Me and my boyfriend met at work and have been dating a few months. He had a first on me for over 6 months while I was in another relationship. He’s really respectful and treats me like a queen but now I’m starting to think not so much. There’s this girl that We work with that has had a crush on him and flirts with him. We try to keep things private and she isn’t one of the people who knows we’re going out. Most of the time he’s not flirty and is kinda rude to her, but tonight they were exchanging flirty banter, RIGHT IN FRONT OF ME. To me that’s like a slap in the face. It’s one thing to be cordial, but another to be flirting. By the way she was responding she thought he was flirting with her too. Is this a legit reason to be mad? Because I might just drop him from this my ex used to do this all the time and it’s bad deja vu