The flu virus is not transmitted through your bloodstream or your breastmilk. However, you can spread the flu virus to your baby because of the close contact with the baby.
Therefore, don't sneeze or cough on your baby. Wash your hands immediately after blowing or wiping your nose.
Mothers with the flu should carry on breastfeeding whenever possible. The reason to continue breastfeeding is simply because, in general, "breast is best". A mother's antibodies against diseases are transmitted to her baby through breast milk.
Babies aged six months to two years have almost no resistance against any serious diseases. Breastmilk is in general, a good way to boost your baby's immune system before the age of three years.
If a nursing mom takes medication containing antihistamines (often used in flu medication), it may affect the baby through the breast milk. Antihistamines should be avoided.