I agree that doxxing flat earthers should never happen and privacy is important.
I think you came on very strong in your reply to him which may have been why he refused to continue the discussion though. I wonder if he didn't realise his own actions were contradictory, or if he simply and naively thought asking for others identities in his mind didn't mean doxxing but simply giving credentials to his topics and who he's speaking to or about. Or maybe he actually does realize what he's asking and his intentions are ill.
I guess the best course of action would be to raise awareness to anyone he intentionally or unintentionally doxxed so that they can ask him to take any information down should they so wish, which I suppose is what you're doing here.
there's not much else you can do other than that, the individuals themselves would need to take action if they were doxxed.