If my fiance was discharged (administrative) after just entering Navy boot camp will he be eligible for re-entry?

He is probably receiving not an administrative discharge, but rather an "Entry Level Separation." Under personnel regulations, when a service member has been on duty for less than 180 days and something comes up which prevents them from continuing their service past that point, they receive an "ELS." Usually an ELS will not bar a person from re-enlisting so long as they have remedied the issues which brought them into the ELS in the first place. As far as taking 2 to 3 weeks to out-process him from Navy Boot camp, that should correct to me. Remember, it took several weeks of process and paperwork to get him in the Navy and it will take some time to get him out too. Typically when someone is ELSed in boot camp, they are removed from the training environment and placed in a holding unit. They may have to perform light physical labor - not punishment - to occupy their time while the out-processing is underway. Once he goes into this "casual status" she will probably be able to phone you more often.