Translation:ko kākou hae
Indeed, kāua, kākou, māua, or mākou could be correct here, given that there is no context. I will add the following as alternates for this sentence:
ko kākou/kāua/māua/mākou hae
ka hae o kākou/kāua/māua/mākou
It might take a little while for the Duolingo system to update, but they should be accepted after that.
Prefacing with the comment that there are exceptions to the rules which we may never "understand" given the language and people group are much older than any of us, I will speculate that a flag, banner, crest, or other clan/family insignia is something a person is born under, or born into. Either way, it is not something you acquire, but like your family, heritage, and very own body, it is "O" class.
This may not be an especially satisfying answer, but I can say that both "o" and "a" are accepted here as possibilities. I tend to see and hear "o" used with "hae", and if I heard "a" used, I would think it was an intentional use to show that the flag was made by the person, for example, I would think "kaʻu hae", "my flag", referred to the flag that I made. It doesn't necessarily mean that the person made it, but that would probably be my first thought.