I'm not entirely sure what some of the other guys commenting here are reading - you aren't being unfaithful; if you were the one persistently flirting, then of course that would make you unfaithful, but you're not doing any of that, right? That's all "Zack."

However, I do believe that you need to be blunt in telling Zack to back off. Your friend-zoning hasn't worked - he thinks there is a possibility that something could happen between the two of you. Assuming he is aware of it, he isn't respecting your relationship, as he continues crossing your boundaries by flirting. Being this guy's friend isn't an option, and trying to keep him as a friend is only stringing him along.

Also, if you haven't already, I would make your boyfriend aware of this situation. You need to tell him that all of this is one-sided and that you have been struggling to let him down gently. If word of Zack's infatuation (or whatever you wish to call this) with you gets out, this whole thing could easily be misconstrued.