in fear of sounding stereotypical ... but flirty girls tend not to be the kind to listen or hope for their parent's approval. She might like that her parents will disapprove of you. Kind of like a taboo.
I say don't worry about the parents, and just try to get with her ... unless you REALLY want to be in a serious relationship with the girl, then u will have to woo her, and then try to impress her parents ... but that might be VERY difficult. Asian parents tend to be stubborn in this category... but in the end it's HER you are trying to impress and be with. If you succeed there, then worry about the parents.