By default you can offer free shipping down to State level but not down to individual zip codes. It may be something a developer could sort out for you as I have seen one or two requests here for the same.
I can't I'm afraid but maybe you could have a word with Mike who has done this kind of thing in the past I believe https://www.ecommercetemplates.com/support/pop_profile.asp?mode=display&id=2195