Should questions about learning to speak a language using a different accent be on-topic? For example, someone who is already a fluent speaker of English might ask for information on how they can learn to speak English with a Brooklyn accent.
Yes, learning an accent (often called accent reduction) is an important part of language learning, and is entirely on-topic here.
If one is a native speaker of the target language, and just learning a new accent, it's still language learning, and I see no reason to exclude it.
Yes, such questions should be allowed. Learning a language always involved learning a specific accent. This may be the "standard" or mainstream accent for a specific language, but it needn't be.
In addition, questions about learning a specific accent have a clear scope and can be answered in "how-to" style, and these are two characteristics of constructive questions.
However, asking just about the features of a specific question would be off-topic.