Is it permissible for my brother to marry the daughter of my mother's sister, given that my mother breastfed her (the daughter) to a satiating extent, and my aunt breastfed my brother to a satiating extent?

Your foster sister is your maternal aunt's daughter who was nursed by your mother. She is considered a sister to all the children of your maternal aunt whom your mother nursed. She is also a foster sister to your paternal half-siblings if the suckling was with your father's milk (i.e., from the milk of the male, laban al-fahl), and it does not matter that the nursing woman is not their mother. The suckling must consist of five satisfying breastfeeds. If one of your paternal half-siblings marries this girl, the marriage must be immediately annulled, and the children born from this union are legitimately attributed to the husband.