Would "John's brother-in-law" have been "ko John kaiko'eke?" That was the only reason i could come up with for my getting shot down for typing "John's brother-in-law." I did comment on the flag page that my answer should have been accepted, but then I started wondering whether they might have a reason for insisting on the more complicated English phrase, as much as I'd NEVER use that in actual conversation.
Keoki is John's brother in law... is correct, too. Perhaps more correct idomatically. We don't say "the mother of John", we say "John's mother" The phrase "brother in law of John" is not syntactically correct in English. It reads as if it is a transliteration. I often encounter this in Duolingo, more often in some particular languages than others, but definitely across the entire spectrum of Duolingo language courses. One is forced to adopt the syntactically incorrect translation in order to progress.
I can't tell if your just frustrated and venting (we've all been there) or if you really want to know. But there's probably others who want to know, so I'll answer seriously. This kind of sentence (that starts with 'O) is an equivalence sentence and will have two terms which you are being told are really the same thing. In this case, "Keoki" and "the brother-in-law of John". The difficulty in understanding these sentence is figuring out where the first term ends and the second one begins. The easiest way is to look for a second determiner like ke, ka, kēia, kēlā, ʻo, etc. Those determiners usually begin a new noun phrase, so they can be used to find the break between the two noun phrases in the equivalence sentence. The o without the ʻokina instead connects two nouns together and does not create a new noun phrase. Thus the "ka" right after "Keoki" tell us that the first noun phrase has ended and the second one has begun. "Keoki" is sitting alone and "John" is part of the "brother-in-law" phrase. So while John and Keoki are each brothers-in-law of each other, this sentence is specifically telling us that "Keoki is the brother-in-law of John."
I did dreadfully on the quizzes for family relationships so I have been studying. Here you have two males as brother-in-law. Thus I see kaiko’eke. Easy to remember. But what do you say for a brother-in-law of a female (or a sister-in-law of a male)?
Best source I found so far is https://hawaiian-grammar.org/current/