Kroger’s Pharmacies Are Now Offering Flu Shots. Insurance Plans May Cover The Cost, And The Cincinnati, Ohio-Based Grocer Accepts Medicare. Kroger Also Offers Fluzone Hd For Every Patient 65 Years And Older. The Centers For Disease Control And Prevention Recommends An Annual Flu Shot For All People Age Six Months And Older. No Appointments Are Necessary At Kroger Pharmacies.