This Koan is a perfect example of pointing to suprarationality. It is pointing to an inexpressible nondual state beyond moving and stillness or breeze and flag. The fact that the sixth patriarch says the mind is moving does not mean it is the “answer”. Notice that the flag is always seen on a flag pole. The flag pole is stationary and it is the flag/wind that is seen moving. But all that is a projection of the mind, and this is an example of the idealist conception within Buddhism to say that the mind itself is moving rather than the flag or wind. But really this points to a deeper duality which is stillness and motion. The stillness of the flag pole and the motion of the flag/wind, and the stillness of the mind. Once we reach this underlying duality, then it is a matter of indicating and approximating the indicated nondual state between the two duals.
Flag and wind moving indicates opposition in nature, and that opposition in nature is absorbed into the mind in idealism. But this points to the underlying dichotomy between mind and nature, stillness and movement. What is the nondual between these fundamental states?
The statement of the patriarch is really another question, rather than an answer that points at this nondual state which is not both nor neither or not A nor non-A). The tetralemma exhausts all the logical possibilities, and points to emptiness which is beyond all those logical possibilities. Suprarationality means that the moving and non-moving, subject-object, flag-wind all are simultaneously effective without interfering with each other. It is something that is other than and opposite paradox which would be the mixture of the various contradictory states.
The theory behind Zen comes from Hua Yen Buddhism of Fa Tsang, which recognizes that emptiness is interpenetration. Thus flag and wind, subject and object, nature and consciousness, stillness and movement all interpenetrate but yet each hold their form though their differences.
In general what this koan is really referring to is the difference between karmic function and suchness. The karmic function is the wind, and the concrete manifestation of the aggregate suchness of the flag is its opposite. But they are actually both the same thing and made possible by the alayvijyana or storehouse consciousness that receives the karmic seeds (bija) and stores them until they fructify. How karma could operate in the face of emptiness was always a fundamental problem in Buddhism. But Buddhism was idealistic, not believing in physical nature for the most part. So everything was interpreted phenomenologically from an idealistic stance for the most part. The Patriarch is pointing to this substrate of mind, the storehouse consciousness which is the basis for the interaction of the karmic function (wind) and the suchness (flag). But in the alayvijyana the seeds are still, quiescent. So from a theoretical point of view the question is how the seeds can exist in this quiescent state being embedded in the emptiness. And the answer to that is that the emptiness although nondual still has its own structure that allows it to act as the receptivity and carrier for the seeds of karmic action. There is a part of the mind called the alayavijyana that has this stability even though it is still empty.
A good reference for this is the Awakening of Faith, and also Fa Tsang’s recently translated commentary on it. The interesting thing about this commentary is that it is the only example I can find where there is a self-conscious explanation of the Emergent Meta-system which is the underlying model of karmic quasi-causality.