Jerry explained to you yesterday what 'under four different flags' means. Why are you posting the question again?

It can vary largely, depending on the context of the question. So, with what you said, can a country be 'under' a flag? I don't think so. 'Using' may be a more correct word. Whatever the case might be, do take note that the word to fill in the gap should be in the 'present continuous' tense. This is because of the 'has been' used in the question. I hope its clear? :)