I think this depends on how flawed the premise are.
Suppose, for example -- and I'm going to use deliberately silly examples because I don't want to get sidetracked in serious debates -- suppose someone asked, "How many animals did Abraham bring on to the Ark?" Well of course it was Noah and not Abraham, and any answer that accepted the false premise and went on to talk about Abraham loading animals on the ark would be wrong. But it would be easy to fix the problem with a sentence, like "I presume you mean how many animals Noah brought on the Ark, in which case ..." and then go on to answer the real question.
But it's easy to imagine questions where the premise is so flawed that the question cannot be answered as stated. Like if someone asked, "How could Jesus have been executed by the Romans when he lived hundreds of years before the Roman Empire existed?", it is difficult to see how one could give a direct answer to the question. The only possible reply is to say that Jesus did NOT live hundreds of years before the Roman Empire existed.
Then there's a middle ground where I think the question becomes tougher. What if someone asks a question based on a premise that is debatable or controversial? Like suppose someone asked, "Given that science has proven that evolution is a fact, there was death and suffering before humans evolved, and therefore before Adam sinned. So how can Adam's sin be the cause of death and suffering?" It seems to me that there are two quite different ways one could answer the question. One way would be to try to reconcile the Christian doctrine of Original Sin with evolution. The other would be to challenge the idea that evolution is true, i.e. to challenge the premise.
To an extent I think this depends on the wording of the question. Suppose the OP acknowledges that a premise is debatable, and then phrases the question as, "For those who are convinced that X is true, how do they reconcile that with Y?" In that case I think challenging the premise would be irrelevant and non-responsive.
But what's the difference? I think a key point is that if they question implies that the premise is universally-accepted fact, the OP may not realize that it is, in fact, debatable. Other users who read the question and see answers that all talk as if the premise was accepted fact may also leave with a wrong impression. But if a question acknowledges that he is starting from a debatable premise, this issue goes away.