I agree, walking her to the car should have been like, "Here, ima walk you to your car" *Hold out your arm for her to link.* Asking is not the alpha male thing to do.
As for the kino part, I usually just Kino whenever i can get a chance to. For example, if i get her laughing, ill just innocently put my arm on her shoulder and laugh w/ her. And then after a while, if you feel like theres a connection, do the "Mystery Knee Test." Cross your legs while shes sitting beside u, take her hand and put it on ur knee. If she moves it off, punish her by saying, "Alright, you're losing me.." or something along those lines and give her the cold body language and look away. Then if she tries to reinitiate the conv, not only is that an IOI, but you can just repeat the leg test, and see if she complies. usually they do. and at this point, whenever u wanna kino lightly, you can just touch her hand thats on ur knee.

squeeze and w/e you wanna do with it.