Had a mild allergic reaction to diflucan (fluconazole) will the medications still work?

No answer. "Mild allergic reaction"??????What is that????? Yes, it will still reduce the population of yeasts. MOST, not all, but MOST of the time a person thinks they are "allergic" to a med they are mistaken. Unless you provide details about the "mild" reaction, I will assume that you are not sensitive to fluconazole.
You should. Not taken Diflucan (fluconazole) if you are allergic to it. Do not use any drug from the class of drugs called azole antifungals. Rec.: see a prescribing physician a medicine adjustment.