inappropriate friend

My friend gets inappropriate around my guy On fb when I post and tag him she right away always has to comment on stuff he tags me in too.  But usually only when he comments. I've noticed.   One day I had posted a food I cooked so he wrote yum , she writes under I'm coming over , he replies "no "in a playful manner.  With a emoji wink face and a few other emojis . She wrote back don't be greedy save me some.  He then wrote nope.   She replied ooh tell your man to stop being greedy.   Check him.   But there's a few more like that.        Latest one I posted a pic with different candies . Choose A , B, C, D she writes in a comment after my guy chooses his fave candy she writes D because I like getting the D. He "lol" comments .    She's always been a flirt and has been known to mess with guys taken or not.   My guy is a flirt on his own.  Would you be annoyed that your friend always has something to say on fb after your guy comments or replies to him.  In a flirty "try to be funny" way . They've never met. Would u prevent them from meeting by not inviting to baby shower? She's done this in the past to one of my exs while I was dating him. I also made the mistake last month telling her he's a major flirt and can't be trusted.