"Those who are in the flesh cannot please God. But you are not in the flesh; on the contrary, you are in the spirit, if only the Spirit of God dwells in you. Whoever does not have the Spirit of Christ does not belong to him. But if Christ is in you, although the body is dead because of sin, the spirit is alive because of righteousness. If the Spirit of the one who raised Jesus from the dead dwells in you, the one who raised Christ from the dead will give life to your mortal bodies also, through his Spirit dwelling in you." (Romans 8:8-11)
St. Paul, when referring to "the flesh" in this passage is not writing about the body. If he was simply referring to the body he would've used the Greek word soma. Instead, he uses the word sarx. Before unpacking this term a little bit, it is important to note that a truly Christian anthropology is not dualist, meaning that we do not see the body as something evil, as something to be overcome, to be set aside, to be escaped from. On the contrary, we will be bodily resurrected and live forever as embodied beings. Rather, God created us as we are, redeemed us through the bodily sacrifice of His Only Begotten Son, who for our sake became incarnate in the womb of the Blessed Virgin, His bodily resurrection from the dead, and His bodily ascension into heaven. He now sets about sanctifying us in our bodies by the power of the Holy Spirit- Just think about the sacraments! All of this is necessary because the temptation to gnosticism is ever present and has been from the beginning!
Like most every word in a lot of languages sarx has a number of meanings. In its most straightforward, that is, literal sense, sarx (i.e., "the flesh") refers to the soft substance of the living body, which covers the bones and is permeated with blood. It also means the sensuous nature of humankind, what we might call our animal nature. According to just about any New Testament Greek lexicon, sarx, which is used in the writings of St. Paul to refer to our sensuous nature, does not automatically suggest depravity, but does refer to those bodily cravings that lead us to sin if we follow them unchecked in a hedonistic manner.
A great example of the distinction St. Paul makes in this passage is found in Matthew 26:36-41. This passage is Matthew's account of Jesus' prayer in the Garden of Gethsemane. Before laying bare His soul before His Father, our Lord says to Peter, James, and John- "My soul is sorrowful even to death. Remain here and keep watch with me." Going off to pray and asking the Father to let the bitter cup that He is about to drink, even the dregs, the Lord returns to find the three fast asleep. His disappointment and sorrow are evident when He says, "So you could not keep watch with me for one hour? Watch and pray that you may not undergo the test. The spirit is willing, but the flesh is weak." It is not difficult to imagine the three, when asked by Jesus to keep watch with Him, responding positively. I further imagine it growing later, colder, darker, making them even more tired. So, huddling together, they warmed up and, perhaps even fighting their drowsiness, fell asleep. If you follow the passage, they fall asleep more than once! Hence, St. Paul's constant injunction to wake up, to stay awake, etc.
It is good that we hear this late in Lent, a season in which we try to open ourselves to God by more intensively practicing the spiritual disciplines, putting off the flesh through acts of self-denial in order to live according to God's life-giving Spirit (i.e., "the Lord, the giver of life"). In this passage from his Letter to the Romans, St. Paul sets forth something James Kushiner summarizes very well: "What the discipline is meant to do is to help you get yourself, your ego, out of the way so you are open to His grace." I think "flesh" in the sense Paul uses it in this passage can certainly be called "ego".