Sweetie, he sounds like he’s either callous or has shallow feelings. Or, an insecure man.
It’s OK for you to feel sensitive and have unpleasant feelings about the flirting, if you’re a couple. You said you’re mutually attracted to each other. There are many, many men that do not do that.
Also, it can depend on how serious the relationship is and even the environment. Flirting happens in bars and clubs, a lot, for example.
Communication is key. Talk to him using “I” sentences.
“I” feel uncomfortable and ignored when you flirt with another woman.