Using the rhetorical question, James indicates that God is jealous in the sense that He is concerned and involved in the Holy Spirit that He has placed inside of believers. Another way to look at it is that God takes our decision not to trust Him very personally if we continue to live according to the wisdom of this world. 
Having placed His Spirit within us, He will not easily allow us to pursue lives of self-service and self-reliance. The deepest desire of God is for us to walk in spirit and truth and conduct ourselves in a way that is pleasing to Him. As each of His children grows, He desires that they would conform to the image and likeness of His dear Son day by day.
We should not allow our human spirit to lust for the things of the flesh, nor should we allow fleshly pride to prevent us from living as God desires. Rather than being influenced by the things of this world, we should humble ourselves under God's mighty hand as we die to our own desires and live a life that honors Him.

Dear Heavenly Father, it is such an amazing privilege to have the Holy Spirit dwelling in us, who desires us to be holy because You are holy. Help me never to nurture carnal attitudes or crave for the things of this world. Keep me from strife and acrimony. Let me seek first the kingdom of God and His righteousness and be mindful of my brothers and sisters in Christ. May I truly die to my own desires and live with Your praise and glory in mind. 
In Jesus's name I pray. Amen.