Have a sit down, all three of you and get everything on the table. Explain the situation and the reason for the sit down (For you the goal should be show to your bf that this is a matter of concern to you personally)
Someone is lying and chances are it is the girl. No mater what the outcome of the sit down is. Tell your bf that it is his choice what he wants to do with this girl and you will stay out of it. If he continues doing what he does (I.e. flirting - because it requires a recipricator) as if nothing happened then I don't think he is as nice, sweet and honest of a person as you described him. And maybe you should start thinking if he is the right guy for you...
Don't cry, don't regret and don't blame
Weak find the whip, willing find freedom
Towards the sun, carry your name
In warm hands you are given
Ask the wind for the way
Uncertainty's gone, your path will unravel
Accept all as it is and do not blame
God or the Devil
~Born to Live - Mavrik~