As you might expect, different flavors appear to take a different amount of time to enter breast milk. In one recent study, researchers gave breastfeeding mothers capsules of banana, caraway seed, licorice, or menthol flavor, and tested their breast milk to see when the flavors arrived and when they left.
Banana peaked and was gone within an hour. Caraway and licorice peaked in two hours and diminished after that. Menthol remained at fairly stable levels from about two to almost eight hours. The timing varied a fair amount from woman to woman, but all four flavors were gone from all of their breast milk by eight hours after the mother swallowed the flavor.
Learn more in Feeding Baby Green Chapter 6, The First Months
Hausner, H., et al. “Differential Transfer of Dietary Flavour Compounds into Human Breast Milk.” Physiology and Behavior, 2008, 95: 118–124.