Q: If I were to flip cards from this effect and only have one or two cards in the discard pile, where do the cards go afterward?
A: This is a rare scenario, since if you truly had no cards in discard and were unable to flip enough to be able to choose 3 cards in your discard pile, that’d mean there are an abundance of your cards in your hand or in play. Regardless, when this does occur, you simply follow the rest of the text in order: if you only can choose one card, your opponent puts the card in your hand. If you choose two cards, your opponent puts one in your hand and the other is buried.
Ruling: Although this says “Your Opponent puts one in your hand.” This is still considered an action performed by you to remove a card from the discard. This is relevant in terms of Jaucq Ee, and Young Bucks Gimmicks. Thus your opponent chooses the card but it is you yourself moving the card.