There is a lot of fail here but I'll help as best I can.
- After girl A shot you down, why would you ask again? I know us guys can hold out hope and think to ourselves "one last attempt" but it's always going to go south.. in the future, let the girls chase you.
- Then you go out with girl B. She knows girl A and you get with girl B. You're now thinking that girl A might change her mind on you now that girl B wants you.. there is SOME truth to that but not much.
- Girl A has already decided in her head that you are below her (hence you chasing her) and you dating girl B will just result in her (girl A) think she is above the girl you are dating (girl B).
- So all you'll really accomplish is further enhancing girl A's view of herself, downgrading girl A's view of girl B, and keeping you right where you are (Below girl A).
The only thing you can do to win this situation is to floor girl B with affection and awesome dates to the point that girl A becomes jealous of all the nice things you're doing for her friend that is "below her". BUUUUT if girl A becomes jealous, she'll likely f*ck everything up with you and girl B by telling her friend that she went out with you and you weren't up to par for her. There is an outside shot that girl A will then try and steal you away (after all, she views herself as superior) but would you really want her if she does stuff like this?