The Flesh is here almost portrayed as a character, or creature with its own desires. Those desires may continue, but they will not be gratified -- a thirst unslaked, a hungry belly left to ache because you are distracted from these desires by walking by the Spirit, enjoying intimate conversation with Christ.
This sentence is written as if a certainty...not a way to up your chances of behaving well, but a guarantee that the desires of the flesh will go wanting, and you will not feel the loss. It's more tautological than a prescription. This is just what happens to those who walk by the Spirit: with eyes fixed on Jesus, they forget to feed their pet gremlin (the flesh).

Galatians 5:16