Deine Schwester wohnt aber nicht in Kiel, oder?
I would suggest that it means "Your sister doesn't live in Kiel, right?".
But the aber is a real pain. I looked everywhere on the Internet and nothing seems to help me.
The "aber" probably really just means "but" here.
But your sister doesn't live in Kiel, does she?
So it indicates that the answer that you expect ("She doesn't live in Kiel") somehow contradicts what has been said before or would otherwise be unexpected.
So, for example, imagine that a friend reports meeting his sister in Kiel. But you think you remember she lives elsewhere, which makes that more surprising.
"Gestern war meine Schwester zu Besuch."
"Deine Schwester wohnt aber nicht in Kiel, oder?"
"Nein, sie wohnt in Hamburg, aber das ist nicht sehr weit."
It's not limited to negative questions, either. "Deine Schwester wohnt aber in Hamburg, oder?" would also make sense.
Your translation is correct but it would also be correct if aber was missing from the original. What it can signify here is the speaker thinking of something or questioning an assumption they made. If this is the context, you could carry it over in translation like this:
Wait, your sister doesn't live in Kiel, does she?
Another reason for putting aber in such a question would be disapproval of that possibility, should it be true, whether that is because they consider the possibility below their standards or because it would complicate things in whatever context it was raised.
I think the more pronounced "Your sister does not live in Kiel, does she?" might match it a bit better (although i am a native german speaker, not english, so i might be wrong). The "aber" here usually is a request for clarification, or a hint at a misunderstanding or confusion. It most likely means that the speaker previously held the impression that the sister indeed lives somewhere else, and something was just said that cast a doubt on this assumption.
I think in this case it depends too much on the previous sentence. If I were to translate it maybe I'd try a more freely translated version:
However, your sister doesn't live in Kiel, does she/right?
Das ist eine Abtonungspartikel, wie bloss oder doch.