It does not preclude that we do not have a nature of flesh.Those who have crucified the flesh, with the affections and lusts, (Gal 5:24), now have a divine nature.
Thanks be to God !
Gal 5:16, This I say then, Walk in the Spirit, and ye shall not fulfil the lust of the flesh.
I am in agreement with you that we do not have to walk according to it.