What happens to a spell that is cast with flashback when it gets countered by a Remand?
A spell that was cast using Flashback will always be exiled, no matter how it left the stack

702.33. Flashback
702.33a Flashback appears on some instants and sorceries. It represents two static abilities: one that functions while the card is in a player’s graveyard and another that functions while the card is on the stack. “Flashback [cost]” means “You may cast this card from your graveyard by paying [cost] rather than paying its mana cost” and “If the flashback cost was paid, exile this card instead of putting it anywhere else any time it would leave the stack.” Casting a spell using its flashback ability follows the rules for paying alternative costs in rules 601.2b and 601.2f–h.