So, I checked the ESV and KJV for the words "final authority" being together. They are not. So, no where in the Bible does it say the KJV is the final authority, because the words are just not there. No Bible version is the "final authority." But Jesus is!
So I checked on the word "authority" in this case, exousia. Here is what I found.
"And it came to pass, when Jesus had ended these sayings, the people were astonished at his doctrine:29 For he taught them as one having authority, and not as the scribes." Matt. 7:28-29
"And Jesus came and said to them, “All authority in heaven and on earth has been given to me." Matt 28:18 ESV
"And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth."KJV.
Hmm! Both versions are right! Jesus has πᾶσα ἐξουσία or "pasa exousia" which is all power or authority.
Maybe this is your problem John? You do not realize Jesus has all authority, not a translation?
So I checked on the word "authority" in this case, exousia. Here is what I found.
"And it came to pass, when Jesus had ended these sayings, the people were astonished at his doctrine:29 For he taught them as one having authority, and not as the scribes." Matt. 7:28-29
"And Jesus came and said to them, “All authority in heaven and on earth has been given to me." Matt 28:18 ESV
"And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth."KJV.
Hmm! Both versions are right! Jesus has πᾶσα ἐξουσία or "pasa exousia" which is all power or authority.
Maybe this is your problem John? You do not realize Jesus has all authority, not a translation?
So if we talked about the Final Authority we simply talked of the Written Authority, the scriptures.
When Jesus was tempted by the devil, used the word (the scriptures) as his Final Authority.
Interestingly, compare your ESV with the KJV in this instance what really represent the true reading as found in Luke 4:4, Did Jesus say as in ESV is the correct one? or it is the KJV that does say it properly. A simple cross-reference to what Christ quoted, seem ESV failed the test.
KJV Luke 4:4 And Jesus answered him, saying, It is written, That man shall not live by bread alone, but by every word of God.
ESV Luke 4:4 And Jesus answered him, “It is written, ‘Man shall not live by bread alone.’”
KJV Deut. 8:3 And he humbled thee, and suffered thee to hunger, and fed thee with manna, which thou knewest not, neither did thy fathers know; that he might make thee know that man doth not live by bread only, but by every word that proceedeth out of the mouth of the LORD doth man live.
ESV Deut.8:3 And he humbled you and let you hunger and fed you with manna, which you did not know, nor did your fathers know, that he might make you know that man does not live by bread alone, but man lives by every word[fn] that comes from the mouth of the LORD.