I ran into "how would you be knowing that?" when reading a novel. I did a search in Google Books.
It seems to be a fairly productive use:
“And how would you be knowing that?” “Billy's your brother and I heard you calling him Billy James. Not an amazing piece of deduction, I assure you.” “You're quick with your mind, you are. Or at least you'd have me believe."
"You're hiding something from me," said Margaret, frowning. "It was Mr. Morton, wasn't it?" Hilda's eyes grew round. "How would you be knowing that?" "I was on the corner when he came here. I saw him.
“And how would you be knowing that?” Beth countered bravely. “My Mummy told me!” Paige said haughtily. “You don't think I would ever let a man touch me without a huge valuable engagement ring on my finger do you?”
I think the use of would here exhibits the speakers' surprise.
But why would the continuous infinitive be used instead of the bare infinitive of know?
Know is a stative verb which isn't normally cast into an ing-form.