You probably do flirt, I think everyone does in their own way. And not always when it's someone they fancy, sometimes it's just to get what they want from someone, for example. Maybe this person is a bit shy?
From what you've said I do think they're interested in you, another thing to look out for it if they ask you loads of questions, then remember everything you say, but recall it in a way that makes it seem that they don't quite remember, when they can. So that they're pretending not to remember to look 'cool' about it. Does that make sense?