The battle of Bunker Hill (June 17, 1775) was the first full-scale battle between British troops and rebel colonists. The rebels had fortified Breed's Hill, which overlooked Boston. If cannons could be placed on the hill, they could shell Boston and drive the British out. General Howe formulated a plan to drive the colonists from their fortifications.
Some of the British were to feint (that is, to pretend to attack) the redoubts, while the elite grenadiers and light infantry were to push through a rail fence and outflank the redoubts. Unfortunately, Howe's plan bogged down when the grenadiers and light infantry attacked the fence. Colonel John Stark's militia fired on them, and instead of pushing on, the British stopped to open fire. When this happened, Stark's men inflicted heavy casualties on the British.
With the grenadiers and light infantry decimated, and the outflanking maneuver a failure, Howe had to force the redoubts front-on. He succeeded, but at an immense cost to the British army.
From this battle, the rebels believed that the British would attack earthworks head-on. This cost them dearly at Long Island, where the same General Howe outflanked them and drove them away from New York.
As for the British, they used outflanking maneuvers in many battles, and generally won. At Long Island, Brandywine, and Camden, the British successfully outflanked their enemy.