A player called a Flower for an exposure but picked up a 1 Bam by mistake. Nobody else at the table noticed the error and the game continued. This player later declared Mah Jongg and the error was noticed. Is this player's hand 'dead'?

Yes, this player's hand is dead. It is each individual player’s responsibility to pick up the correct tile when making an exposure. As the player had an incorrect exposure when declaring Mah Jongg, their hand is dead.