One possible plot could be that Charlie comes back to Hogwarts for some reason, maybe to help with a dragon - related problem. Hermione, being the brilliant witch she is, is also involved in the solution. As they work together, they start to develop feelings for each other and eventually share a kiss. Maybe it's a moment of celebration after they successfully solve the problem.
In a different plot, there could be a magical accident that causes Hermione and Charlie to swap memories or some part of their personalities. As they try to figure out how to reverse it, they have to spend a lot of time together. During this time, they get to know each other on a deeper level. Charlie is impressed by Hermione's intelligence and Hermione is drawn to Charlie's adventurous spirit. The kiss could be a moment of realization that their feelings for each other are real, despite the strange circumstances that brought them together.