Trust me, guys don't know how to flirt. If they do it goes wrong. (See Friends - Episode when Ross tries to flirt with the pizza girl).
Before making a decision, you have to find out if girl A like you. Ask through one of her friends, like girl Bs friend did.
Someone said use girl B as a back up. Perosnally, if I had any respect for girls, I wouldn't do that. It's not fair on them. But if girl A isn't interested, see how things go with girl B.