The Church is the proper authority. The person would be interviewed by a representative of the Bishop. The prophecy would be examined in terms of the teachings of the church and Tradition as well as Scripture.
Ultimately, if necessary then the claim would go to the Congregsation for the Doctrine of the Faith (CDF) for a final opinion. There has been a recent example of exactly this route in the “Lady of All Nations” prayer which supposedly was given to the visionary Ida Peerdeman in 1952. The Bishop of Haarlem (Netherlands) declared in 1996 that the prayer was authorised. However, there are several things unclear about these visions of Peerdeman and several Bishops conferences from around the world have subsequently sought clarification.
In this prayer Our Lady is invoked as Lady of all Nations “who was once Mary”. Ida Peerdeman claimed that BVM appeared to her in 1951 and supposedly said: " Many people have known Mary as Mary. Now, however, in this new era which is about to begin, I wish to be the Lady of All Nations."
This implies giving Our Lady a new name, which of course would be very contrary to Church Dogma and Tradition. In this light we have to be careful with any “Private Revelation”. Such revelations can bring a new light of faith to the faithful but they may not add or detract from the faith as we have it handed down to us from the Apostles. The Church is clear on this, that God has Revealed himself to the world in His only Begotten Son, Christ and that this revelation “died with the last Apostle”. So there can be no “new” revelation. But there can be new understandings of that revelation.
