We have seen weathercocks fixed on tall towers to indicate the direction of the wind. A weathercock is essentially an arrow free to rotate on a horizontal plane about a vertical axis. It has two fins symmetrically placed on either side of the rod forming the arrow.
As the wind blows, the arrow turns and faces the direction of the wind. If the arrows does not face the wind, the pressure exerted by the wind on one fin will be lesser or greater than that on the other. Consequently the cock is forced to rotate up to a position in which the force acting on the fins are equal and opposite, is reached.
This argument can be extended to a flying flag. When the flag faces the wind, the wind blows from edge which is secured by the rope to the free edge. As it blows, the flag is subject to frictional drag. Friction is a reaction force and, in this case, it acts in a horizontal direction opposite to that of the wind force. Depending on wind turbulence (the changes in the wind speed and direction) the horizontal component of the frictional force on the flag moves from one side to the other. This causes fluttering.