Here are scriptural examples of Paul walking after the flesh, post salvation:
Romans 7:
7 What shall we say then? Is the law sin? God forbid. Nay, I had not known sin, but by the law: for I had not known lust, except the law had said, Thou shalt not covet.
8 But sin, taking occasion by the commandment, wrought in me all manner of concupiscence. For without the law sin was dead.
The above statement of fact is in direct accord with Jesus' Facts from Matt. 15:19-20, Mark 7:21-23 and Matt. 5:28. Paul is ALIGNING himself with Jesus' TRUTH in the above, and not in DENIAL of Jesus' Facts. It's called "evil thoughts" which defile us. They are not OPTIONAL. They are a direct result of sin coming into contact with THE LAW, which then spurs internal resistance. This is Christian understanding, 101.
There is a mountain of more evidence of Paul walking in the flesh. So let's open our own eyes to the obvious, shall we?
Romans 7:
15 For that which I do I allow not: for what I would, that do I not; but what I hate, that do I.
I'd insert a "ding" here for the above just to draw people's attentions to the fact of it.
Romans 7:
19 For the good that I would I do not: but the evil which I would not, that I do.
So, in one brief chapter, we can observe Paul having evil thoughts, doing what he hates and doing evil. I could go on at length with even more observations of this matter, but if a reader can't pick up on the obvious above they never will.
Salvation is not and can not be hooked to ourselves or our works. The above facts show and prove WHY this is not and can not be the case.
The path Paul brings us down by using the LAW is directly into the cold hard facts that we are not going to avoid the conclusions of being sinners, present tense, REGARDLESS of any "good actions." This path that Paul takes us down brings us all directly to the condemnation of Romans 8:3.
And Paul then employs these facts to show a TWO FOLD state.
One, that the flesh body is DEAD because of the very real facts of sin indwelling the flesh and evil present therein, Romans 8:10, which are by the way adverse spiritual workings. These things, indwelling sin and evil present with us are NOT forensic. They are the result of the "spirit of disobedience" operational in the flesh. Mark 4:15, Romans 11:8, Romans 11:32, 2 Cor. 12:7, 1 John 3:8. As distasteful as it is, our sin, yes, ours, is connected to the devil, quite clearly. We are called OUT from pawnship to that working, but we can, will and do contend with it every single day of our lives in the flesh. And yes, it is operational, as PAUL HIMSELF shows us, by many personal examples.
The point of this is twofold. We do walk in the flesh, having sin, evil present, quite active because we are engaged with perpetual warring therein, Romans 7:23. This warring even extends to various forms of blind disputes among us all, as is entirely obvious.
These things are condemned by God in Christ. Whether active or passive.
Nevertheless, our SALVATION is in Him, OF HIM, not of ourselves. Which is the general point. Every "works salvation" proponent is blind to the obvious problems with that posture. They are only kidding themselves about the facts above, vainly trying to justify what can not and never will be justified or justifiable.
Condemnation is A GOOD THING to apply to ourselves, to our own flesh. It is an excellent instrument to keep indwelling sin and evil present in CHECK.
Now, who wants a nice steaming hot plate of condemnation? Any takers? No, it's not a pleasant meal, at first bite. It is one that is only savored over time because it brings us a critical state of humbleness. We dare not lift our head above HIS.