It doesn't really conflict if you think carefully about it. The fruit of the Spirit is all in the way we behave and conduct ourselves toward others and in general. It is not a transfer of any kind of power between one person and another. Radiating the fruit of the Spirit is in the order of other seeing your good works and glorifying God. When we show the fruit of the Spirit in our conduct toward the unsaved, it causes conviction of sin, because every person has a conscience, whether they want to admit it or not, or whether they obey it or not. Conviction of sin can cause a person to move toward Christ as the gospel is shared with them, or they become angry and want to shut you down because they don't want to hear the gospel or the inner voice of their conscience.
But when a person believes that they have some sort of power within them that they can transfer to others, then they are moving into the occult and witchcraft, because the Holy Spirit doesn't work that way. When the prayer of faith is prayed for another person, that prayer in itself is not some force that does anything to that other person. Nor is it a demand on God to do anything. Prayer is a request to God to do what He is able to do according to His will. Because God is sovereign, we can make a request on behalf of ourselves or others, but He does what He thinks is most appropriate in the circumstances. According to Philippians 4:6-7, the immediate effect of making a request to God is receiving the peace of God that passes all understanding. There is no guarantee that the request will be granted, because God is not obligated in any way to us and any request we may make. He is totally sovereign and we cannot demand anything of Him.
The laying on of hands is a demonstration of faith. It is not a transferring of power. It is our request in faith that God gets on that person's case and does in and for that person according to His will. When we see some healing evangelist laying hands on a person, clenching his teeth and screwing his eyes tightly shut as if transferring some kind of power is an effort, what we are observing is just play acting and theatre. When I pray for a person, I take them by the wrist as a point of contact with the view that we are agreeing together in our request to God to do His will.
Therefore, I can take hold of the person's wrist and say, "Jesus heals you" as an act of faith, and then the outcome is completely in God's control. Then the peace of God that passes all understanding comes to both of us.
A healing evangelist telling someone if they believe hard enough the answer will come, is saying total nonsense. It is more akin to pagan Hindu mind control as if the answer will come by the power of the mind. Norman Vincent Peale's Positive Thinking is at the heart of this, and he was a self-confessed believer in occult mind control techniques. Robert Schuller was one of his principle disciples, and Kenneth Copeland is also a proponent of positive thinking and confession to achieve what we want from God. They believe that positive thinking will succeed, but negative thinking will block the answer. This is all pagan mind-control. In fact God was very negative in His thinking when he told Adam and Even that if they ate of the tree of the knowledge of good and evil they would die! Jesus was the same. He said that if we hate our brother we are in danger of hell-fire! How negative is that!