My first read through of your post, my impression was that you overreacted to something that may or may not have meant anything. You saw a message from an old friend/ex of hers, demanded to see the rest of the conversation, and she complied with what you describe was a "dramatic" ultimatum. It's not surprising that she felt weird about that - hence the hesitation. There was no smoking gun in the conversation. You have your own explanation of her 'boring' comment already. You felt that some of her comments were flirtatious, but you also acknowledge that she is a person who craves flattering attention - my guess would be that either she doesn't see these things as flirtatious, or they were said only to get that hit of attention and not intent to cheat. I hope that you were being vulnerable and explaining that you needed reassurance, rather than interrogating her about her social life and who she sees. A little hard to tell tone off a computer screen.
You said she doesn't have respect for your relationship and hasn't been honest with you. What did she actually say or do that was dishonest or disrespectful? She says she hasn't cheated with this guy, or anyone else, and you don't have any knowledge otherwise. She told him no in every message you saw. She told him she was in a relationship. She even offered to stop talking with this guy to make you feel better. To which you respond that she can still talk to/see him BUT you still don't trust her?
My advice would be, if you think you can get over this, then yes, you should put it behind you and trust her. Assume that everything she told you is the truth. I'd also suggest, since she offered, to take her up on not talking with this guy anymore - but make it clear that it's because you're insecure, not because you don't trust her to control herself with him. Giving her more time/attention is something else you'll need to communicate about to make sure you're both getting your needs met. Like most things in a relationship, it's all about communication.
If you can't do that, then yes, do yourself and her a favor and end it.
And as always for anonymous internet advice, if I've read anything into your post you didn't intend, feel free to ignore :)