One of my best friends was in the same situation a few months ago and everything worked out fine
I am sure that nothing will be going on with them, he is dating you and if he liked anyone else more than you then I'm sure he would be with them instead of you.
I think you have nothing to worry about. If your best friend is a natural flirt then surly you can expect it from her? Talk to her about it and tell her you dont like how flirty she is with you boyfriend and if she is truly a best friend she will understand.
Hope everything works out for you.
me if you ever need a chat