What is it to be in the flesh? It is to be in relationship with God on the ground of our natural responsibility as men, as children of fallen Adam. It is, as to our moral state — which in itself is true — making the disposition of God towards us to depend on what we are towards Him. Of this the law is the perfect rule. It says, if conscience is awakened, I am such and such: God will be so and so towards me. Grace is on the opposite ground: God has been, and is, through Christ such and such, and I shall be so and so, as the fruit of it. But this changes everything."On Sealing with the Holy Ghost", Collected Writings of J. N. Darby, Volume 31, p. 260
The key to the transition from Romans 7 to Romans 8 is "in the flesh" vs. "in the spirit" (Romans 8:5–8). This is probably the most succinct description of what it means to be "in the flesh" I have ever found.
And of course, virtually all "christian" teaching I come across is nothing more than treating believers as "in the flesh". It's like trying to build a house without a foundation (as the Evanescent Free Man has pointed out). Biblical Christianity is entirely based on the idea that Christ has taken our place so that we could take His. When we think like we're just men and women "in the flesh", when we think of ourselves as on probation before God, then we've completely abdicated the place that Christ has prepared for us.
Is that the whole story? Of course it isn't! There are all sorts of things God is doing in us, but it's all based on this one fact: we don't stand before God as responsible creatures. We stand before God "in Christ".