Antonyms for the phrase "flying in the face of" include words like conforming, adhering, following, obeying, and complying. To conform means to comply with rules or standards, while adhering refers to sticking or clinging to something. Following refers to moving in the direction of a particular goal or objective, while obeying means to comply with authority or instructions. Complying implies that one follows rules or regulations set forth by an authority figure or organization. In essence, all of these antonyms imply that one is following the rules or standards rather than defying them as in the case of "flying in the face of.