Rom 7:17 So now it is no longer I who do it, but sin that dwells within me.
Rom 7:18 For I know that nothing good dwells in me, that is, in my flesh. For I have the desire to do what is right, but not the ability to carry it out.
Rom 7:19 For I do not do the good I want, but the evil I do not want is what I keep on doing.
Rom 7:20 Now if I do what I do not want, it is no longer I who do it, but sin that dwells within me.
So you think that the flesh of all people is corrupt?
So you must think that David was in error when he described his body in the following way?:
"For thou hast possessed my reins: thou hast covered me in my mother's womb. I will praise thee; for I am fearfully and wonderfully made: marvellous are thy works; and that my soul knoweth right well" (Ps.139:13-14).
In regard to the verses you quoted we see that at other places that a Christian can either walk after the Spirit or after the flesh:
"That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit" (Ro.8:4).
When Paul contrasts walking in the flesh with walking after the spirit he is speaking about being self-centered as opposed to being God-centered. Paul speaks about that same principle here:
"For they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit" (Ro.8:5).
We can also understand that it is indeed possible for a Christian to walk or live after the flesh because Paul tells Christians that if they live after the flesh they shall die:
"For if ye live after the flesh, ye shall die: but if ye through the Spirit do mortify the deeds of the body, ye shall live" (Ro.8:13).
If it is impossible that a Christian can walk after the flesh then it would make absolutely no sense for Paul to tell Christians that "if they live after the flesh you shall die."
The "death" spoken of here is in regard to the Christian's walk, that "we should also walk in newness of life" (Ro.6:4) so that "the life also of Jesus might be made manifest in our mortal flesh" (2 Cor.4:11). That life ends or dies when a Christian ceases from walking after the spirit and begins walking after the flesh.
The second part of verse 13 is telling Christians that if they mortify the deeds of the body they will live. Christians are already received eternal life so Paul's words there are also referring to walking in newness of life.
From all of this we can understand that Christians can indeed walk in the flesh and when they live or walk that way they cannot please God. The Apostle John refers to that kind of walk as walking in darkness:
"This then is the message which we have heard of him, and declare unto you, that God is light, and in him is no darkness at all. If we say that we have fellowship with him, and walk in darkness, we lie, and do not the truth" (1 Jn.1:5-6).
Besides that, if the flesh of all people is corrupt and vile then that can only mean that the Lord Jesus was also made with the same kind of flesh because He was made like His brethren "in all things":
"Wherefore in all things it behoved him to be made like unto his brethren, that he might be a merciful and faithful high priest in things pertaining to God, to make reconciliation for the sins of the people" (Heb.2:17).