The flu vaccine has a lactation risk of L1 (Saftest).
This means that it is the safest type of drug to take while breastfeeding.
The following is taken from the book, Medications and Mothers' Milk by Thomas Hale:
"Influenza virus vaccines come in two forms. One that is non-viable and requires injection, and the second, a live but attenuated vaccine for application in the nasal passages (FluMist). Injectable (Flu-immune, Fluogen, Fluzone, etc.): This influenza vaccine is prepared from inactivated, non-viable influenza viruses and infection of the neonate via milk would not be expected. There are no reported side effects, nor published contraindications for using influenza virus vaccine during lactation. Influenza vaccine is now indicated for breastfeeding mothers and their infants by the American Academy of Pediatrics. Intranasal Live Influenza Virus Vaccine (FluMist): This vaccine consists of a live but attenuated and heat unstable form of influenza virus. Virus instilled in the nasal mucosa replicate thus producing immunity in the host. Virus that escape the nasal mucosa are unstable and die quickly. It is not known if this virus reaches the human milk compartment, but it is highly unlikely the virus could survive at this temperature in the plasma nor the milk compartment of the mother. The CDC and the FDA recommend that all breastfeeding women be immunized. This will further protect the breastfed infant as these antibodies will pass into milk, and help protect the newborn breastfed infant from infection. Contents of influenza vaccines change from year to year. Presently, the multi-dose vials contain a small amount of mercury, but there is no evidence that this would even pass to a breastfeeding infant. Single dose vials do not contain mercury. The live attenuated vaccines, FluMist, are not recommended for breastfeeding women, although we know the risks are low."