rear admiral vs flag officer

rear admiral and flag officer both are nouns.

Word	Noun	Adjective	Verb	Adverb
rear admiral	Yes	No	No	No
flag officer	Yes	No	No	No

As nouns, flag officer is a hypernym of rear admiral; that is, flag officer is a word with a broader meaning than rear admiral:

rear admiral (noun)	flag officer (noun)
an admiral junior to a vice admiral	a senior naval officer above the rank of captain