Chi An's innate nature is to fight, however, her upbringing/society pressure makes her bury this personality. She tries her hardest to please her surroundings, pretending to be someone she is not. The Dragon boy is a free spirit and he brings this hidden personality of hers out. This is the biggest reason of why she felt the most comfortable around him. She could just be herself.
So, honestly, it depends on the situation. Think of Chi An as someone oppressed because of how deeply-rooted Confucious teaching in ancient China. Women of that era were expected to behave in a certain way. As such, the idea of Chi An being an aggressive flirt is unlikely, also Tian Zhao shows no interest in other girls but herself, so the whole jealousy thing is also unlikely. Tsundere, well, not really, though in the beginning, Chi An does not see Tian Zhao favorably because of his brazen attitude. But she comes to love how unrestrained his spirit is. For someone as restrained as Chi An, she seeks freedom more than anything, and she could only feel so whenever she is with Tian Zhao.
As for combat, she doesn't know how to fight, but is more athletic than average women.
I hope that helps
It's best if you try the demo if you want to get a better feel of the characters.