This exact phrase "desires of the flesh" is used in the Bible, or very similar phrases, depending on the translation. Looking at it in context:
Galatians 5:16-24 (ESV)
¹⁶ But I say, walk by the Spirit, and you will not gratify the desires of the flesh. ¹⁷ For the desires of the flesh are against the Spirit, and the desires of the Spirit are against the flesh, for these are opposed to each other, to keep you from doing the things you want to do. ¹⁸ But if you are led by the Spirit, you are not under the law. ¹⁹ Now the works of the flesh are evident: sexual immorality, impurity, sensuality, ²⁰ idolatry, sorcery, enmity, strife, jealousy, fits of anger, rivalries, dissensions, divisions, ²¹ envy, drunkenness, orgies, and things like these. I warn you, as I warned you before, that those who do such things will not inherit the kingdom of God. ²² But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, ²³ gentleness, self-control; against such things there is no law. ²⁴ And those who belong to Christ Jesus have crucified the flesh with its passions and desires.
"The flesh" in this passage is in contrast to "the Spirit". The works of the flesh are sinful desires and passions, whereas the fruit of the Spirit is a list of virtues and disciplines.