The next description of these filthy dreamers involved their flesh. Peter says that they "walk after the flesh in the lust of uncleanness". These "chiefly" are reserved for judgment. Jesus said "the spirit indeed is willing, but the flesh is weak" (Mat. 26:41). Paul spoke of the infirmity of our flesh and our tendency to yield ourselves the servants of uncleanness (Rom. 6:19). In Romans 8, led in from the back of chapter 7, Paul gives an explanation of what we are in the flesh and what it takes to overcome the flesh. Not relying on God, these ungodly men walk after the flesh and fulfill their own lusts. But Paul is very clear to put on Christ and not make provision for the flesh and lusts (Rom. 13:4). Not only do they walk after their flesh, but these certain men defile their flesh. Their temples that they have been given by God are corrupted by their practices (Rom.12:1). This likely goes back to "turning the grace of our God into lasciviousness".
The application: We are not to walk after the flesh either, nor defile it. What's more, Paul says in Eph. 6:12 that "we wrestle not against flesh and blood..." Our enemies are not these false teachers, when they can be won, as Jude says later. Rather it is Satan and his minions.