From Longman Dictionary of Contemporary Englishfly the flagfly the flagto behave in a way that shows that you are proud of your country, organization etc → fly
Examples from the Corpus
fly the flag• And take it down: Hotel is told it can't fly the flag.• Elsewhere, Orrell are flying the flag for top flight northern rugby in their own, inimitable style.• The monk is alleged to have flown the flag from the roof of the monastery.• That power can be exercised only with regard to vessels flying the flag of the member state concerned or registered there.• The hotel has been ordered to apply for approval to fly the flag, or take it down. 