Giacomini played right tackle at Louisville and started all 12 games last season. He was Green Bay's fifth-round selection.
Flynn was selected in the seventh round. The quarterback led LSU to last year's national championship. He was the second quarterback selected by Green Bay this year; Brian Brohm was chosen in the second round.
Swain was Green Bay's second selection in the seventh round. The wide receiver led San Diego State with 58 catches for 973 yards and five touchdowns.