Flirty conversations in an otherwise healthy relationships...am I being insecure?

Hey all, Not totally sure this is in the right forum, so just let me know if I need to move it... edited for tl:dr - gf has been having flirty conversations (mostly one-way) with an ex, whilst in a committed relationship. I'm annoyed she doesn't tell this guy where to get off. What should I do? I've been in a pretty great relationship for the past 10 months and I recently moved in with my SO. It was quick, but we spend so much time together and thought it was the right thing to do. We're very open for the most part, and I don't think we hide much from each other...but I noticed something the other day that made me feel a little insecure. We share a computer, and often sign each other in an out of email and FB (the snoopers dream ticket, I know right...) but we have nothing to hide so it's never been an issue. Anyway, whilst the gf was out, I went to sign in to FB but noticed a message from a random guy who I had never heard about, which seemed kind of odd as she doesn't have a problem talking about past relationships or when guys are hitting on her. Anyway, I thought about just closing the conversation, as I've never once in previous long-term relationships in checked a partners phone or email, and never had suspicion to either. But the one message was pretty sexually explicit from this guy... The short of it is that I opened the conversation and it seems like this guy is an ex (maybe just a fuck buddy?) from a few years ago, and has been hitting on my gf with pretty provocative messages for the past few months, timed every few weeks or so. Her replies were always pretty innocuous, she either laughed them off or, at the very worst said the guy was attractive when he started hitting on her. Numerous times he goes on about how attractive she is, even suggesting a 'last fuck before marriage', which she rejected saying she 'loved me, and would never do that as I am good for her'....but then replied 'glad to to know you'd be down ;)'. I don't have any reason to suspect she's cheating, but it seems pretty inappropriate for someone in a committed relationship to not tell this guy where to get off. Maybe I'm a different type of person as I tend to cut all my ties with exes after a split, whereas she often remains friends with them. Different folks, different strokes. I don't have a problem with that, as she's always been open about it, but it's weird she never mentioned this guy. So basically I don't know if I'm being incredibly insecure and overreacting, or have a legitimate grievance, with either this guy, my gf or both . I was tempted to confront this guy about it, but then he would probably tell my gf I saw these messages. I don't feel comfortable confronting my gf either....and I'm not the snooping type generally, so don't want to become paranoid and start checking these things again in future...so how do I approach this? Any advice would be great!

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