What causes a flag to wave in the wind?

Friction.

http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/fric.rxml


But....If you have to ask, you would not understand.

Wind is the movement of air from an area of higher pressure to an area of lower pressure. Those differences of pressure are a result of the uneven heating of the Earth’s surface. When the difference between high and low pressure is greater, the winds will be stronger.

When a Low pressure system moves Easterly, it is replaced by a trailing High pressure system. The wind will rush out of the High system to fill the area vacated by the moving Low system. The greater the differences in pressure between the Low and the High, the stronger the wind will blow!


http://www.universetoday.com/82329/what-causes-wind/

Its flexibility, and slight variations in wind speed. Sometimes at higher wind speeds, an areodymanic flutter effect.
https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.107.194502