My NARCISSIST ex use to pull this stunt on me until I put a stop to it. If we were in a store and he noticed a woman eyeing, he would make sure to tell me. He would suggest she was my competition, I would just shrug it off and handle my business. One day while we out, he was really feeling himself and decided to flirt one lady that was following us around the store. I gave her and him one look, she went on her way and this fool was just a grinning. I sent him down a different aisle to pick up something I needed and headed to my car. I had the best laugh watching him chase my car as I pulled off. I eventually let him get in the car, I was very clear, if she want you she can have you.
He stopped that mess that day..... When I look back on that relationship, there were HUGE Red Flags but thank God it is OVER now.