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These verses are helpful for addressing what is commonly described as a "burning in the bosom," which LDS point to as confirmation of the truthfulness of their theology. However, subjective feelings are not the standard of truth. The heart is deceitful, but the Word of God is True. God is unchanging and cannot lie. We must appeal to what He has said to have epistemic grounding and certainty.
It can be effective to point out that many people are very certain about their views of Jesus. Islam teaches that Jesus is the greatest prophet but is not divine and didn't die on the cross, Jehovah's Witnesses say that Jesus is Michael the Archangel, Heaven's Gate taught that Jesus was an alien and they looked to catch a spaceship to heaven. You can also share your own testimony, but the main point to get across is that feelings cannot be equated with truth. God's Word is sufficient and authoritative to settle matters of doctrinal dispute.
The context is that Paul and Silas just got kicked out of Thessalonica for preaching the gospel, and they had moved on to Berea. And though the Bereans did not know Paul and Silas beforehand and had never heard the gospel before, they accepted them and tested their claims by Scripture. We are told they were more noble for this. They are laid out as an example for us to follow. Just like Paul tells us:
LDS website on James 1:5–6: "Reading this verse led Joseph Smith to pray in the Sacred Grove, where he experienced the First Vision (see Joseph Smith—History 1:11–17)."
Joseph Smith cited this verse about going out into the woods to pray before his First Vision experience and receiving new revelation. I point out that the word for wisdom used in this verse in Greek is sophia (like philosophy, philo-sophia, the love of wisdom). It is not gnosis, meaning knowledge. Having pointed out that Scripture is our standard for all claims of knowledge with the previous few verses, it can be helpful to preemptively raise this verse before your interlocutor can (this is a favorite verse of many LDS), and interpret it correctly for them.
James White says, "Hence we see that the Bible does not contradict itself, but does indeed tell us that God’s revealed Word is the final authority, not our feelings or prayers, no matter how strong those feelings, or sincere those prayers."