From the CDC:
Who Should Not Be Vaccinated
There are some people who should not get a flu vaccine without first consulting a physician. These include:
•People who have a severe allergy to chicken eggs.
•People who have had a severe reaction to an influenza vaccination.
•Children younger than 6 months of age (influenza vaccine is not approved for this age group), and
•People who have a moderate-to-severe illness with a fever (they should wait until they recover to get vaccinated.)
•People with a history of Guillain–Barré Syndrome (a severe paralytic illness, also called GBS) that occurred after receiving influenza vaccine and who are not at risk for severe illness from influenza should generally not receive vaccine. Tell your doctor if you ever had Guillain-Barré Syndrome. Your doctor will help you decide whether the vaccine is recommended for you.