flag rank vs military rank

flag rank and military rank both are nouns.

Word	Noun	Adjective	Verb	Adverb
flag rank	Yes	No	No	No
military rank	Yes	No	No	No

As nouns, military rank is a hypernym of flag rank; that is, military rank is a word with a broader meaning than flag rank:

Other hypernyms of flag rank include military rating, paygrade, rating.

flag rank (noun)	military rank (noun)
the rank of a flag officer	rank in a military organization