What is the role of the charismatic prophet and prophecy in the Orthodox Church?
In the Orthodox Church there is no office of prophet (while, I have been told, there is in the Roman Catholic Church). However, we have great respect for the prophetic gift, which in the Orthodox Church is usually called "clairvoyance." That's a tough word for Protestants because it is the word commonly used to refer to pagan fortune tellers. However, the word just means the ability to know by personal revelation what would not normally be known.
The Orthodox Church does not generally focus on charismatic office, but does honour charismatic function. So for example, we do not have an office (or title) of Apostle. However, we recognize certain saints as being "equal to the Apostles." That is, we say that their life manifested the Charism of Apostolic ministry. We do not have in the Church the office of "healer." However, we recognize "unmercenary healers." We do not have the office of "prophet," yet we expect to hear from God when we speak to our spiritual fathers/mothers.
All of the charismatic gifts function freely in the Church, but they do not function in the haphazard, make-it-up-as-you-go sort of way they do among the Protestants (I speak from personal experience as a Pentecostal-Charismatic Protestant for the first 36 years of my life). Within the Orthodox Church personal holiness is key to discerning the prophet. That is, if the healer, prophet, preacher or whatever does not live a holy life, does not preach the Orthodox faith or does not submit to the bishops, then we do not pay any attention to him/her--regardless of how powerful his/her miraculous power appears to be.
Another important difference between the way charismatic giftedness functions in the Orthodox Church and the way it apparently functions among the Protestants is that the Orthodox ethos does not generally promote miracle workers until after they have fallen asleep in the Lord and their whole life can be evaluated. Of course you can always find an exception somewhere; however, the charismatically gifted Orthodox Christians I have known or heard about take the words of Jesus litterally: go and tell no one (Mark 7:36). We do not put miracle workers on T.V. Most commonly, those with the greatest and most powerful spiritual gifts are hidden most from the eyes of all but a very few and the very humble. For example, they may hide themselves in hermitages, or they may appear to be somewhat insane ("Fools for Christ's sake"), or they may be generally despised because of their unwillingness to cooperate with those who are powerful in this world (St. John Maximovich is a good example here).
Only after their deaths, when they cannot be corrupted by human glory and the holiness of their life is manifest, do their charisms become widely known. Since death does not hinder the Grace of God, the gifts that are given to these holy men and women continue to be poured out through their intercessions after they have fallen asleep. This is one of the many reasons why we "pray" to the saints--or more exactly, ask for their intercessions. God has given them charisms for the Church, so we ask them to continue to pour them out on our behalf through their intercessions to God with and for us.
So their are indeed holy prophetic or clairvoyant men and women in the Orthodox Church. In fact, I encourage you to expect your spiritual father or mother to speak to you prophetically. Keep in mind, however, the words of St. Paul that you must discern these words, accepting what is good and letting go of what isn't. No prophet, even the most holy "God-bearing" elder, gets it all right every time ("we have this treasure in earthen vessels"). Our own faith and our discernment interacts with the gift of God in the holy man or woman.