John 5:39 where He said, "You search the Scriptures because you think that in them you have eternal life; it is these that testify about Me; 40 and you are unwilling to come to Me so that you may have life." The Lord is essentially saying, "you don't get eternal life from the scriptures, you get it from me, yet you are stuck in a very bad place of believing the scriptures is where you get this life".
The problem with this is that they only had the old testament.
The Old Testament existed to tell of the coming Christ. I disagree with your conclusion of this passage. I think Jesus was saying you search the old testament scriptures that tell of me, and I am right in front of you and you do not see me. It was not that they believed they received life from the scriptures, but that they did not see the very person it is pointing too standing in front of them. The Bible is all about Christ
Christ is the sum total of all that God has spoken to man. The final expression of this is contained in the book of Revelation which was given by God to Jesus and then to John [Rev.1:1]. This is God’s final revelation about His Son and the Son’s final revelation which He gave to His apostle [Rev.22:16]. Anyone who adds to this final revelation will come under the judgment of God [Rev.22:18,19].
The sufficiency of the Bible is evident because its subject is Christ in whom dwells all the fullness of Deity in bodily form [Col.2:9]. God has spoken to us in His Son whom He has appointed heir of all things [Heb.1:2].