What James does not say is, "Are any of you sick? Pray a prayer of faith and you will be healed".
Nor does he say, "Are any of you sick? Let them call for the elders and they will pray a prayer of faith and you will be healed".
The Rx that Dr. James prescribes is this:
[Jas 5:14-16 NLT] (14) Are any of you sick? You should call for the elders of the church to come and pray over you, anointing you with oil in the name of the Lord. (15) Such a prayer offered in faith will heal the sick, and the Lord will make you well. And if you have committed any sins, you will be forgiven. (16) Confess your sins to each other and pray for each other so that you may be healed. The earnest prayer of a righteous person has great power and produces wonderful results.
- call for the elders
- they will invoke the name of the Lord while rubbing oil on you
- they will pray over you
- that kind of prayer/ritual will result in your healing
James invokes the example of Elijah, suggesting it might take earnestness and persistence in prayer:
[1Ki 18:41-45 NLT] (41) Then Elijah said to Ahab, "Go get something to eat and drink, for I hear a mighty rainstorm coming!" (42) So Ahab went to eat and drink. But Elijah climbed to the top of Mount Carmel and bowed low to the ground and prayed with his face between his knees. (43) Then he said to his servant, "Go and look out toward the sea." The servant went and looked, then returned to Elijah and said, "I didn't see anything." Seven times Elijah told him to go and look. (44) Finally the seventh time, his servant told him, "I saw a little cloud about the size of a man's hand rising from the sea." Then Elijah shouted, "Hurry to Ahab and tell him, 'Climb into your chariot and go back home. If you don't hurry, the rain will stop you!'" (45) And soon the sky was black with clouds. A heavy wind brought a terrific rainstorm, and Ahab left quickly for Jezreel.
In the ministry of Jesus, he healed those who approached him for healing in the manner described in the prophet Malachi, which was to touch the hem of his garment:
[Mal 4:2 NLT] (2) "But for you who fear my name, the Sun of Righteousness will rise with healing in his wings [IE: the fringes of his garment]. And you will go free, leaping with joy like calves let out to pasture.
[Mat 14:36 NKJV] (36) and begged Him that they might only touch the hem of His garment. And as many as touched it were made perfectly well.
[Mar 6:56 NKJV] (56) Wherever He entered, into villages, cities, or the country, they laid the sick in the marketplaces, and begged Him that they might just touch the hem of His garment. And as many as touched Him were made well.
Does Mark 5:27-28 contain an allusion to Malachi 4:2?
So to obtain the healing prescribed by James one must comply with the ritual outlined. Faith, per James, is demonstrated in obedience:
[2Ki 5:1-19 NLT] (1) The king of Aram had great admiration for Naaman, the commander of his army, because through him the LORD had given Aram great victories. But though Naaman was a mighty warrior, he suffered from leprosy. (2) At this time Aramean raiders had invaded the land of Israel, and among their captives was a young girl who had been given to Naaman's wife as a maid. (3) One day the girl said to her mistress, "I wish my master would go to see the prophet in Samaria. He would heal him of his leprosy." (4) So Naaman told the king what the young girl from Israel had said. (5) "Go and visit the prophet," the king of Aram told him. "I will send a letter of introduction for you to take to the king of Israel." So Naaman started out, carrying as gifts 750 pounds of silver, 150 pounds of gold, and ten sets of clothing. (6) The letter to the king of Israel said: "With this letter I present my servant Naaman. I want you to heal him of his leprosy." (7) When the king of Israel read the letter, he tore his clothes in dismay and said, "This man sends me a leper to heal! Am I God, that I can give life and take it away? I can see that he's just trying to pick a fight with me." (8) But when Elisha, the man of God, heard that the king of Israel had torn his clothes in dismay, he sent this message to him: "Why are you so upset? Send Naaman to me, and he will learn that there is a true prophet here in Israel." (9) So Naaman went with his horses and chariots and waited at the door of Elisha's house. (10) But Elisha sent a messenger out to him with this message: "Go and wash yourself seven times in the Jordan River. Then your skin will be restored, and you will be healed of your leprosy." (11) But Naaman became angry and stalked away. "I thought he would certainly come out to meet me!" he said. "I expected him to wave his hand over the leprosy and call on the name of the LORD his God and heal me! (12) Aren't the rivers of Damascus, the Abana and the Pharpar, better than any of the rivers of Israel? Why shouldn't I wash in them and be healed?" So Naaman turned and went away in a rage. (13) But his officers tried to reason with him and said, "Sir, if the prophet had told you to do something very difficult, wouldn't you have done it? So you should certainly obey him when he says simply, 'Go and wash and be cured!'" (14) So Naaman went down to the Jordan River and dipped himself seven times, as the man of God had instructed him. And his skin became as healthy as the skin of a young child's, and he was healed! (15) Then Naaman and his entire party went back to find the man of God. They stood before him, and Naaman said, "Now I know that there is no God in all the world except in Israel. So please accept a gift from your servant." (16) But Elisha replied, "As surely as the LORD lives, whom I serve, I will not accept any gifts." And though Naaman urged him to take the gift, Elisha refused. (17) Then Naaman said, "All right, but please allow me to load two of my mules with earth from this place, and I will take it back home with me. From now on I will never again offer burnt offerings or sacrifices to any other god except the LORD. (18) However, may the LORD pardon me in this one thing: When my master the king goes into the temple of the god Rimmon to worship there and leans on my arm, may the LORD pardon me when I bow, too." (19) "Go in peace," Elisha said. So Naaman started home again.
So is there any significance in the anointing with oil? The oil being prescribed, I believe, is the balm of Gilead:
http://jewishencyclopedia.com/articles/2414-balm
[Jer 8:21-22 NASB] (21) For the brokenness of the daughter of my people I am broken; I mourn, dismay has taken hold of me. (22) Is there no balm in Gilead? Is there no physician there? Why then has not the health of the daughter of my people been restored?
Modern science confirms that the balm of Gilead has bone fide healing properties:
Chios mastic gum (Pistacia lentiscus var. Chia, Anacardiaceae): A review:
...CONCLUSIONS:
Chios mastic's beneficial properties have been demonstrated in the treatment of gastrointestinal disorders, wound healing, skin inflammations, plasma lipid and blood sugar reduction and oral care. These properties are attributed to triterpenes and volatile compounds. However, because of the resin's chemical complexity and the lack of commercial standards for its main compounds, there is a notable gap in literature concerning the biological evaluation of CMG's isolated components. Therefore, future research should focus on the development of efficient extraction, isolation and analysis techniques in order to unravel CMG's full pharmacological potential.
https://www.ncbi.nlm.nih.gov/pubmed/32092498
So to answer the question, the prayer of faith involves obedience by both the petitioner and the elders to the details of James' words.