fly in the face of vs fly in the teeth of

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

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

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

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