According to Catholicism, how can a Christian be freed from the concupiscence of the flesh and thereby possess a sinless body? After the fall of Adam &amp; Eve from pride &amp; disobedience, all mankind inherit original sin.

The Catholic Church teaches that the original sin can be removed by the Sacraments of Baptism but the stain of original sin or the concupiscence of the flesh still remains.

St. Paul describes this in Romans 7:15-24 as;


  "I do not understand what I do. For what I want to do I do not do, but what I hate I do. And if I do what I do not want to do, I agree that the law is good. As it is, it is no longer I myself who do it, but it is sin living in me. For I know that good itself does not dwell in me, that is, in my sinful nature. For I have the desire to do what is good, but I cannot carry it out. For I do not do the good I want to do, but the evil I do not want to do—this I keep on doing. Now if I do what I do not want to do, it is no longer I who do it, but it is sin living in me that does it.
  
  "So I find this law at work: Although I want to do good, evil is right there with me. For in my inner being I delight in God’s law; but I see another law at work in me, waging war against the law of my mind and making me a prisoner of the law of sin at work within me. What a wretched man I am! Who will rescue me from this body that is subject to death?


In light of this dilemna, is there a way to remove concupiscence or wash-away the stain of sins in our bodies. Does Christ leave the Church with any teaching how to remove or wash away the stain of sins after we are cleansed by baptism?

Unfortunately, this is a tough challenge for many striving Christians as we can see from Scriptures, Christ has elevated the definition of adultery:


  "You shall not commit adultery," Christ spoke of adultery in the heart. "Everyone who looks at a woman lustfully has already committed adultery with her in his heart" (Mt 5:28).


Now, I'm looking for Church teachings on how to remove concupiscence, as clearly based on Saint Paul himself as he overcame concupiscence when he exclaimed;


  "I have been crucified with Christ, and I no longer live, but Christ lives in me. The life I live in the body, I live by faith in the Son of God, who loved me and gave Himself up for me. (Galatians 2:20)


So, its not hopeless for us. 

**My question is how did Saint Paul overcame concupiscence, and what does it mean when Saint Paul overcame concupiscence his body is sinless like Adam &amp; Eve?
In Galatians 2:20, you quoted shows that faith in the Son of God plays the critical role in overcoming concupiscence.  Indeed, we know very well that Ephesians 2:8-9 provide the precise formula for spiritual salvation: we are saved by God’s gift of grace which is a function of faith:


  For by grace you have been saved through faith, and that not of yourselves; it is the gift of God, not of works, lest anyone should boast. - (Ephesians 2:8-9)


The verses naturally throw up two questions:


What is precisely the faith referred to in Ephesians 2:8?
Given that one’s deed (action or performance, as opposed to words) is not a prerequisite for God’s gift of salvation grace, how then does one say or proclaim this faith and to whom should one proclaim this faith?


We can argue that the Lord's Prayer, authored by no sinful mortal but by Jesus Christ himself, is the foremost proclamation of faith that is referred to in Ephesians 2:8;  that in praying the Lord’s Prayer daily, we are in fact proclaiming our faith or belief that the Son fulfilled the will of the Father. Thus, the Lord’s Prayer encompasses the teachings and exhortations of Paul the Apostle - (Romans 10:8–10, New KJV):


  But what does it say? “The word is near you, in your mouth and in your heart” (that is, the word of faith which we preach): that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved. For with the heart one believes unto righteousness, and with the mouth confession is made unto salvation. - (Romans 10:8–10)


An excellent source is the book "The Creed of Christ: An Interpretation of The Lord's Prayer" by Gerald Heard (1889 - 1971). A well-known author, philosopher and lecturer, Heard studied history and theology at the University of Cambridge, graduating with honours in history. He lectured from 1926 to 1929 for Oxford University's extramural studies programme. More information about him can be sourced from Wikipedia.

In the book, Heard describes The Lord's Prayer as the "real creed of Christianity." On page 6 of his book, he writes:


  At the heart of the Gospels there is, however, one other thing. Beside the new Commandments, beside the new Law, more lovely but far more exacting than the old, there is, put more briefly and tersely, a master-instruction, a set of key-rules as to how that Law may be kept. There is only one passage in the biographies more central than the Sermon on the Mount. It is more central because it is the root from which the action ordered by the Sermon must spring, because it shows the source of power without which the Sermon, the Beatitudes, remain a magnificent but impossible demand, a splendid promise which cannot be fulfilled. That passage is therefore rightly called by a supreme title, the Lord's Prayer. 


Heard goes on to link faith and the Lord's Prayer (for example, as implied by the following passage, page 94):


  It is so against the grain of our present nature to realize that any right prayer must first and foremost be something which alters the self, a process whereby desire is transcended and the will transmuted."Bread of the Coming Day...My bread is to do the Will of Him Who sent me." How are we to do that will which is so different from ours? Are we not here involved in a vicious cycle? To live as God would have us live His eternal Life we have to do His will, but to do His will we have to become part of his Life. As long as we are self-willed, motivated by our wills, we do our wills, not His. 


Through the fulfillment of the will of the Father in His Son, Jesus Christ, the Father declared us righteous in His sight. That is, the death and resurrection of Jesus Christ is our justification, the declaration of God that we are free of guilt and penalty of sin and acceptable to Him - (Romans 4:25, NIV):


  He was delivered over to death for our sins and was raised to life for our justification. - (Romans 4:25)


Our justification also marks the beginning of sanctification, a continual process of being made holy by the power of the Holy Spirit, a lifelong process that makes us more and more like Jesus Christ.

Therefore, the Lord's Prayer is a means to justify ourselves to the Father. Via the Lord’s Prayer, prayed daily, we are led by the Holy Spirit in our daily lives and become more like Jesus Christ – the precise outcome of sanctification.