Unless otherwise noted, Scripture quotations are from the New American Standard Bible, 1995 edition.
Living by the Spirit rather than living by the flesh is a central theme of the New Testament. Much of Galatians 5 is devoted to the subject, and it could be argued that the whole letter is summed up in "Are you so foolish, having begun in the Spirit, are you now completed in the flesh" (Gal. 3:3). In Romans, walking by the Spirit in chapter 8 is the answer to the sin problem in chapter 7 (esp. 8:2-4).
More practically, how to overcome the flesh and its desires is the greatest battle most Christians face. Supposedly, our old man was crucified with him, and the "body of sin" is done away with so that we are "freed from sin" (Rom. 6:6-7). Often, though, the old man seems quite healthy, and the "body of sin" gives us fits!
I have an answer for you.
The New International Version, and perhaps others, uses "sinful nature" rather than "flesh" in several places in the New Testament. Even where it does not actually use "sinful nature,' such as in Galatians 5, the NIV adds a note saying:
In contexts like this, the Greek word for flesh (sarx) refers to the sinful state of human beings, often presented as a power in opposition to the Spirit" (Gal. 5:13, footnote).
This translation is a problem on two levels. First, in several verses, it makes no sense. For example, in Romans 8:3, we read that God sent his Son in the likeness of "sinful flesh." If we used "sinful nature" there, we would have "in the likeness of sinful sinful nature." At the end of the same verse, we would have "he condemned sin in the sinful nature."
Second, if we read through Romans 7, we will see that the problem is not that our flesh is sinful nature. Instead, sin itself "produced in me all kinds of coveting" (v. 8). Sin itself "revived" (v.9). Sin itself "deceived me, and through [the commandment] killed me." Paul's conclusion is that "If what I don't desire, that I do, it is no longer I that do it, but sin which dwells in me." Therefore, when he gives the answer to this problem in Romans 8:3, he says Jesus condemned "sin in the flesh," not the flesh itself.
Once we come to Christ, the "body of sin" really is done away with and we really are freed from sin (Rom. 6:6-7). What we are not freed from is our flesh, which is not our sin nature, but literally our flesh, i.e., our body.
Before you were a Christian, your bodily desires were empowered by sin which dwelt in you. Romans 7 describes the slavery this produces. We want to do what is good, but we cannot. By the end of the chapter, he cries out, "Who will deliver me from this body of death!"
Some Christians believe that the answer to this question is "no one." They believe that Romans 7 is describing Paul's experience as a Christian. That idea would contradict both Romans 6 and Romans 8. Paul's answer to the question is, "Thanks be to God, Jesus is going to deliver me from this body of death" (Rom. 7:25 in my words). He then spends Romans 8 explaining just how Jesus delivered us from this body of death.
He delivered us by condemning sin in the flesh and giving us the Holy Spirit. He did not condemn the flesh, which is our body, and which we must have to live in and interact with this world. Our body has desires, some of them very strong desires, but those desires are no longer empowered by the sin which used to dwell in our flesh.
We still need to overcome the desires of the flesh. Now, though, the sin that made your body master over you has been condemned. You have been given the Holy Spirit to "put to death the deeds of body" (Rom. 8:13). Jesus broke the power of sin so that would have no mastery over you, gave you the Holy Spirit, and now your job is to put to death the deeds of the body through the Spirit. The situation this creates is:
The flesh sets its desire against the Spirit, and the Spirit against the flesh; for these are in opposition to one another, so that you may not do the things that you please. (Gal. 5:17)
This is the situation we are in, but do not misinterpret this verse. The verse before, Galatians 5:16, says that if we walk by the Spirit, we will not fulfill the desires of the flesh. In verse 17, Paul is saying that we cannot overcome the flesh by our own power, but we most certainly can by the power of the Spirit.
Not only can we overcome the flesh by the power of the Spirit, but we must. In Galatians 6:7-8 we are told that if we sow to the flesh, we will reap corruption. Only those who sow to the Spirit reap everlasting life.
Paul writes something similar in Galatians 5:19-23 for the same purpose. There he lists the "works" of the flesh and the "fruit" of the Spirit. If we do nothing, if we make no effort to walk by the Spirit, then we will do the works of the flesh. If we "practice"—make a habit of—the deeds of the flesh, we will not inherit God's kingdom. If we walk by the Spirit, we will find ourselves not fulfilling the desires of the flesh but producing the fruit of the Spirit.
This is why Paul taught, "I discipline my body and make it my slave, so that, after I have preached to others, I myself will not be disqualified" (1 Cor. 9:27).
We must understand, though, that our fight is not to overcome the flesh by our own strength. We must walk by the Spirit of God, and the flesh will be left behind. Fortunately, Paul is very clear about how to walk by the Spirit.
Those who are according to the flesh set their minds on the things of the flesh, but those who are according to the Spirit, the things of the Spirit. For the mind set on the flesh is death, but the mind set on the Spirit is life and peace. (Rom. 8:5-6)
The battle is in our minds. What do we think about? What are we pursuing?
Paul tells us to "be transformed by the renewing of our mind" (Rom. 12:2). He tells us to "set our minds on things above, where Christ is, seated at the right hand of the Father" (Col. 3:1). He tells us that although we can only behold the face of God "as in a mirror," as we behold him, we will be transformed into that same image (2 Cor. 3:18).
The battle is in our minds. What are we thinking about? What is first and foremost in our thoughts. Let us pull out our "divinely powerful" weapons and "destroy speculations" and "take every thought captive to the obedience of Christ" (2 Cor. 10:4). Let us "put on the Lord Jesus Christ and make no provision for the flesh in regard to its lusts."
The story is told of a man in frontier Alaska who would bring dogs in to fight each week. People would bet on his dogs, and one day someone asked, "Do you know which dog will win?"
He answered, "Sure do. The one I fed all week always beats the one I didn't feed."
I do not support dog fighting. I have had dogs as pets throughout my life, and I would never treat a dog that way. That said, the illustration is accurate. Are you thinking about spiritual things, or are you making provision for the flesh? The one you feed is going to win, and according to Galatians 5 and 6, eternal life and our inheritance in the kingdom of God are at stake. Let us make our spirits fat and full of the Holy Spirit and the words of God, which are our true food (Matt. 4:4), and let us starve the flesh of the thoughts and sights that make it strong.