The body of sin is not the physical flesh,
Scripture shows a much different picture from that.
You an look at every time a word appears, and you will find some that are crystal clear from their context what they are talking about, and others simply use the word, but without particular identifying characteristics.
"Once we knew Jesus according to the flesh, but now we know Him that way no longer", that's an example. What 'the flesh' means here is not shown in the context.
Colossians 1:24 KJV
24) Who now rejoice in my sufferings for you, and fill up that which is behind of the afflictions of Christ in my flesh for his body's sake, which is the church:
Here the context is the physical affliction suffered by Paul.
Colossians 1:21-22 KJV
21) And you, that were sometime alienated and enemies in your mind by wicked works, yet now hath he reconciled
22) In the body of his flesh through death, to present you holy and unblameable and unreproveable in his sight:
Here, body and flesh both mean exactly what they seem, the physical flesh body.
Acts 2:30 KJV
30) Therefore being a prophet, and knowing that God had sworn with an oath to him, that of the fruit of his loins, according to the flesh, he would raise up Christ to sit on his throne;
Here, flesh refers to the physicallity of our being. That according ancestry as accounted in the body, that is, who was born from whom.
I assert that in all cases where you look at the word flesh - sarx - you will find this to be true, that all contexts where a specific use is shown that they refer to the physicallity of our being. Our body, the fleshiness of our bodies, the things that pertain to the body. And "body" - soma - will show two uses, the spiritual body of Christ, and the physical body of man.
If we hold to the meaning given by usage in the Bible, that's the meaning, and when we apply that meaning generally, we find a harmony throughout.
Much love!