Is it permissible for my brother to break off the engagement and leave the girl with whom he recited the Fatiha, due to discovering flaws in her that were not disclosed until after the dowry was determined and the marriage agreed upon?

The defects that must be disclosed before marriage are those that prevent sexual intercourse, or repulsive or contagious diseases. What was mentioned about the girl does not contain anything that needs to be disclosed. If she is religious and your brother approves of her, then it is preferable to complete the marriage. If he does not desire her after learning these matters, then there is no blame upon him for dissolving the engagement.