… even though the term “flesh” originated as an anthropological term, in Paul these two phrases have become primarily and essentially eschatological. They describe two kinds of existence: one that belongs to and is conditioned by the present age that is passing away; the other describing our new eschatological existence set in motion by Christ and the Spirit.
Basic to Paul’s view of things is that, as with Torah observance, the time of the flesh is over. Living according to the flesh belongs to our existence before and outside of Christ; it is totally incompatible with life "according to the Spirit."
… Through the work of Christ and the Spirit, God has ushered in the coming, messianic age. Since for Paul the main evidence of that reality is the gift of the eschatological Spirit, it was easy for him to describe present eschatological existence as "in keeping with/according to the Spirit." The natural contrast to this way of describing present existence was to refer to life in the old age as "in keeping with the flesh." But “flesh” now denotes not simply humanity in its creatureliness vis-à-vis God, but humanity in its fallen creatureliness as utterly hostile to God in every imaginable way. Thus, what began as a purely anthropological term in the physical sense, evolved into an anthropological term in a more theological sense (“creatureliness,” thus human frailty), and finally into Paul’s unique usage in a thoroughly eschatological sense. For this reason also, the translation “sinful nature” fails to convey Paul’s meaning, since that tends to make it an anthropological term without adequately recognizing that for Paul it functions principally in an eschatological way. …
Our interest lies strictly with this latter sense (i.e. morally pejorative), which has completely lost its relationship to the physical and has become strictly eschatological—and pejorative—describing existence from the perspective of those who do not know Christ, who thus live as God’s enemies. …
… As far as the believer is concerned, Christ’s death and resurrection have pronounced a death sentence on the “flesh.” As with the “old age” to which it belongs, the “flesh” is on its way out; it has been rendered ineffective through death, which is the meaning of Rom 7:4-6. Through the death of Christ and the gift of the Spirit, “the flesh has been decisively crippled—”killed,” in Paul’s language. … Thus believers live “between the times.” The already crippled flesh will be finally brought to ruin at the coming of Christ. The Spirit, already a present possession, will be fully realized at the same coming. To the degree that the old aeon has not yet passed away, we still must learn ‘to walk by the Spirit,” to behave “in keeping with the Spirit,” and to “sow to the Spirit.” But we do so precisely because the Spirit is sufficient, not because we live simultaneously “according to the flesh” and “according to the Spirit.” In Paul’s view, we live “in the flesh,” meaning in the body and subject to the realities of the present age; but we do not walk “according to the flesh.” Such a way of life belongs to the past, and those who so live “shall not inherit the [final, eschatological kingdom of God” (Gal 5:21).
Source: Gordon D. Fee, ‘The Spirit against the Flesh’ God’s Empowering Presence The Holy Spirit in the Letters of Paul. (Baker Academic, 2009), 816-822.
https://andrewgroves.wordpress.com/2010/11/21/the-flesh/
https://andrewgroves.wordpress.com/2010/11/05/not-in-the-flesh-but-in-the-spirit/
https://andrewgroves.wordpress.com/2010/11/28/romans-7commentators/
Andrew Groves 