The flu virus is not transmitted through your bloodstream or your breast milk. However, you can transmit 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 flu should carry on breastfeeding whenever possible. The reason to carry on 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. Breast milk is in general a good way to boost a 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.