Innapropriate to flirt with guys who are in relationships at work.

My boyfriend of almost 6 years, father of my child, started a new job recently and I am not sure why, but he tells me about women that are (in my opinion) innapropriate.

Such as:

A woman wrote on the white board for everyone to see "I <3 Joey". Idk why women who don't know him call him Joey. His name is Joe don't give him a 'cutsie' nickname.

Aslo, he makes pretty good money, and we have nice cars. So the group is talking about his cars because they can see his out the window, and then (maybe same gal as above) says "I wish you could be my sugar daddy." and in the same day tries to get him to go with her to have lunch.

It is hard to know what really goes on because it is all heresay, but the white board thing I know because he took a picture, and to me that was inappropriate enough. They know he is taken, and I trust him, but it bugs me when people can't respect boundaries. I figure she never would expect me to know about any of this, but I really am hoping to meet her soon. I would almost prefer he just didn't tell me about it, but I feel like he things he is being honest lol