Do babies get antibodies in breast milk after mom gets a flu shot?

Yes: Whether these are really protective for the child is harder to prove. Breastfeeding is a personal decision looking at one's whole life situation. Best wishes.

Not enough: The antibodies in breast milk are predominantly IgA, otherwise called gut antibody, because they help prevent germs from attaching & invading the gut wall. Mothers make IgG after a flu shot, and a little comes across in BM but not enough to be considered protective. If the kid is 6 mo they can get a flu shot.Before then we encourage any of their contacts to get one to "cocoon" baby in protection.