It's grammatical but not logical. Many people don't realize this, but everyone has a specific accent. You might want to ask whether they have a regional accent. If you do, be prepared to hear people deny that they do.Is it native-like if I ask:
Do you have any specific accent?
No. Never. Everyone has an accent. You speak English with a Persian accent. I speak English with an American accent. If you talk, you have an accent.Is it natural to ask: Do you have any specific accent?