fly in the teeth of vs fly in the face of

fly in the teeth of and fly in the face of both are verbs.

Word	Noun	Adjective	Verb	Adverb
fly in the teeth of	No	No	Yes	No
fly in the face of	No	No	Yes	No

As verbs, fly in the teeth of and fly in the face of are synonyms defined as:

fly in the teeth of (verb)	fly in the face of (verb)
go against	go against