What common tool is used to adjust the air shutter in an oil burner?

The correct choice is a flathead screwdriver because it is specifically designed to fit the slotted screws typically used to secure the air shutter in an oil burner. The air shutter adjustment is crucial because it controls the airflow required for proper combustion within the burner. A flathead screwdriver can easily be inserted into the slot of the screw to either tighten or loosen it, allowing for precise adjustments.

While other tools like the Phillips screwdriver, Allen wrench, or pliers may be useful in various aspects of HVAC maintenance, they are not the standard tool for this particular adjustment. Phillips screwdrivers are designed for screws with a cross-shaped slot, Allen wrenches are used for hex screws, and pliers are more suited for gripping or twisting rather than making precise adjustments to screws. Thus, using a flathead screwdriver ensures the necessary control and precision needed for adjusting the air shutter effectively.