A breeze is not "a bunch of air molecules moving in that direction". A breeze is a wave of pressure.
The speed of air molecules is on the same order as the speed of sound. They are flying around smashing into things and mostly bouncing off. You are surrounded by a barrage of minute "meteors" that are smashing into your skin and bouncing off in all directions.
Well, these meteors are mostly bouncing off each other, because at 1 atm things are so dense that the average molecule travels 68 nm before hitting another molecule.
The only thing stopping it from knocking you flying is that you are being smashed into on all sides uniformly all of the time.
A perfect vacuum is just the effect of the other side smashing into you and pushing you that way, without the support of the molecules on the vacuum side. A vacuum cleaner reduces air pressure by a tiny amount, and it causes a pretty huge force this way.
A "wind" is a relatively tiny wave of higher pressure on top of this violet stew of air molecules. We feel it because on the side it is coming from, the pressure is higher, and on the other side it is lower. Even a hurricane is a relatively small change in pressure, and is enough to pick up and destroy houses, trees, cars and people. The strongest hurricane comes from about a 10% difference in atmospheric pressure! That pressure difference from the edge to the center is enough to power the winds of that entire storm.
A 10 km/h wind is traveling at 1% of the speed of sound, which is roughly how fast air molecules move. That macroscopic motion is a tiny contribution to the average kinetic energy of the molecules of air; it has roughly 2% more KE than the same air stationary.
A 100km/h wind is now going at 10% of the speed of sound. As KE is square of velocity, at that point we are talking about 20% more KE than the same air stationary.
You'd have to approach 700 km/h for the wind to have as much KE from its macroscopic "wind" motion as it does from it's microscopic "vibration" motion.
Now, as another poster has mentioned, the velocity of air molecules is actually a touch higher than the speed of sound; sound is a wave, so it isn't going to propogate at the exact same speed as air molecules are (it will travel a bit slower). But it gives you the right order of magnitude.