There is no such thing as "free will of the flesh". Man has will. It's not broken up into various pieces. The body can't make decisions, it is autonomous. You don't decide to digest your food or for the synapses in your brain to fire. Even some bodily functions that can be controlled by sheer effort of will, like breathing, will be overridden even when survival is impossible like underwater. The very fact the lungs of all drowning victims are filled with water shows the body cannot think for itself but is reliant on autonomous functions.
You can't tame your flesh, if we could, we would all think ourselves well from sickness and disease. You control your thinking and where our thinking is wrong it needs to be corrected. This is why we are told to be transformed in our mind. Rom.12:2 Will and thinking are of the soul, not the body. The corruption we know as the sin nature is in the body, not the soul. The soul is in darkness and without truth due to being spiritually dead so the sin nature which, acts on the autonomy of the body and is self serving in nature only (against the Spirit who is the servant of all Mk.9:35 ), deceives the darkened mind. It does not alter the nature of the soul unless that soul willfully embraces the darkness and lies and hence becomes evil. We all are culpable of evil because we are weakened by the flesh and the corruption at work in it but that does mean all willfully embrace evil. This is why when the light and truth of God comes to us and the darkness and lies are dispelled and the sin nature in the flesh is under the control of grace, we can choose what is right because that is the true desire of our souls.
This is how we can be led to Christ (the drawing of the father). If the corruption were in the soul by nature, there would be no hope except to give a literal new soul to a person but then you would no longer be you for who we are as individuals is to be found in our soul.
The purpose of having a will is to live within reality which, is another way to say to live within God's will. We were not created to have spirit, soul and body be separated from each other. You only need look at all the strife and sorrow in this fallen world to know such separation is folly. God originally created man spirit, soul and body as one entity for a purpose, to desire to live otherwise, even for a moment of time, is not wise.