Can I tell a friend/coworker to take responsibility for her failed relationships?
Why do you hold her responsible?
She failed relationships to date, she should break up with her boyfriends instead of cheating on them to avoid hurting them
You should let your coworker deal with their romantic issues on their own. When you meddle in other people's business, you are involving yourself in a situation where the outcome doesn't fall on you.
I'm just going to tell him that she flirts with me, then break up with him.
It is wrong to get involved in your friend's relationships. She may think that you are not a good friend and you will be to blame if something goes wrong.