a "fling" could be a short love (and could be nonsense) relationship with another person. therefore, the "fling" in the statement defines the relationship of the two.
It could be that they had a great time with one another and then went their own separate ways. You've got to understand in the first place that they don't have a legal relationship and that the girl can run away anytime she wants to. A "fling" relationship mostly doesn't lasts.