A screen assembly for a work vehicle is disclosed. The screen assembly may generally include a screen defining a plurality of screen openings for receiving an airflow therethrough. In addition, the screen may define a flap opening. The screen assembly may also include a flap pivotally coupled to the screen at the flap opening. The flap may be configured to be moved to a closed position when the airflow through the screen is in a first direction and to an opened position when the airflow through the screen is in a second direction.