Hi there, and welcome to TeenHelp, Eva! I hope you're able to find the advice you're looking for.
High school is a very exciting time in life. It's a time of self-discovery, and it sounds like you're starting to explore some of that. It's good to examine your thoughts and feelings for what it is you think you might want in life, whether it's what to do for an afternoon without work or school, what future career path you want to take, or what you want out of dating/romantic relationships. It shows introspection and self-awareness and those are good qualities to have!
The thing is, in the scheme of things, fourteen is quite young, and in the next four years SO much is going to shift and change for you. As a result, I don't think you necessarily need to put a label on how you feel about romance and sexuality right now, because I guarantee you that label will probably change at least a little bit. So I wouldn't get too caught up in that, if you can help it.
Unfortunately, I don't think there's really much of a way to start a lasting, stable relationship without the flirting and the breakups, unless maybe you enter an arranged marriage. They're a part of life. I'll tell you right now your first love, should that come along, will probably not be Mr./Ms. Right; in fact, your first few loves probably won't be. From each relationship you learn new things about relationships/dating in general and more about yourself and what you want. It's all a part of the process. Parts of it suck, but, oftentimes it's worth it.
In conclusion, I am not saying you're not greyromantic; you very well may be. But maybe take some time before deciding on a label. It's still perfectly normal not to be interested in dating at age fourteen. It may just be where you're at developmentally and not an indicator of a label.
Good luck, and please
PM me if you need anything else.