1. A truly prophetic ministry will not add to the Word of God.
God has given us 66 books of the Bible, and no more. Jude made it clear that the Christian faith has been once-for-all-time delivered to believers (Jude 3). The apostle John made it clear that God's curse is on anyone who added to or subtracted from his prophecy (Revelation 22:18-19). Paul made it clear that the written word of God is sufficient to equip the man of God for every good work (2 Timothy 3:16-17).
Christ gave the apostles alone the unique authority to bind and loose the Church with His word (Matthew 16:19). The apostles were the foundation of the Christian faith (Ephesians 2:20), and that foundation has been laid. We don't need apostles anymore, because they completed their founding work by writing the New testament.
This means that a Christian who goes to church wanting a "fresh", new word from the Lord, or goes away disappointed that the Lord didn't say anything "new", is thinking like a cultist. How firm a foundation, ye saints of the Lord, is laid for your faith in His excellent word! What more can He say than to you He has said, to you who for refuge to Jesus have fled? To be dissatisfied with the Word of God is a mark of great immaturity.
2. A prophetic-quality ministry will not teach heresy.
This is not to say that a spiritually-gifted man will have infallible doctrinal knowledge. We know in part, and we prophesy in part. But many false prophets have gone out into the world (1 Jn. 4:1).
A preacher who confesses that Jesus of Nazareth is the crucified and risen Christ promised in the Old Testament, and that He is God come in the flesh, is from God. Anyone who denies these truths is an Antichrist (1 Jn. 4:2-3). A preacher who heeds the teachings of the apostles is from God. One who twists or ignores them is not from God (1 Jn. 4:6).
This means that every prophet/preacher must be judged (1 Cor. 14:29). Anyone who claims to be above judgment, or claims to be untouchable because he or she is God's anointed, is a false prophet.
3. A truly prophetic ministry should be controlled by love.
A prophetic ministry without love is nothing (1 Cor. 13:2). This means that a teacher, or prophetic-style preacher, who screams and rants and raves, one who constantly points the finger at others in condemnation, or acts in ways to exalt himself, is displeasing to the Lord. The Lord Jesus was not a ranter.
This also means that being "judgey" toward the Church doesn't mean one is a prophet. The Old Testament prophets didn't just throw stones at Israel. They also preached faith, hope, assurance, and comfort. A preacher who only spits out lacerating condemnations of the Church isn't a prophet, he is just arrogant and self-righteous. The late singer Keith Green was hailed as a prophet, but he later confessed a lot of what he said was just him giving out criticism in a self-righteous, Pharisaical spirit.
4. Along that same line, a Biblically prophetic ministry uses the Word of God to build up. 1 Cor. 14:3.
God reveals to the true prophet an insight from the Word of God, and when he delivers it, all learn and are encouraged, 1 Cor. 14:30-31.
There's nothing uniquely prophetic about telling other people what's supposedly wrong with them. There are abusive people in the Body of Christ who claim to have prophetic ministries, but really they're just chronically critical.
This line can be hard to draw, because the NT prophet might discern hidden needs that others don't see as clearly. The Lord might guide them to address weaknesses that aren't visible on the surface.
Sometimes a prophet will correct and rebuke, because the Word of God sometimes corrects and rebukes. But a true NT prophet wants to build up the people of God. Even when he's trimming the tree, it's so the tree will grow healthier, sweeter fruit. Someone who just loves to tear trees down is not of the Lord.
5. A Biblically prophetic ministry will always be accurate.
Paul in 1 Corinthians 13 says that the gift of prophecy reveals things otherwise unknown. This is different from simple teaching. Also, this is also a unique work of the Holy Spirit that can't be controlled by the person. I know we are wary of this sort of thing. But most conservative writers allow for the Lord to do extraordinary forms of guidance, such as angelic appearance. Spurgeon was no charismatic, but even he recognized the existence of God-given "impressions" that impelled believers to take action at key times.
Agabus by a special action of God knew a famine was coming (Acts 11:28). This was not an inner impression, but a warning to the church filled with intelligible content. It was a guidance warning. He later warned that Paul would be seized in Jerusalem (Acts 21:11). This was also not an inner feeling. It was another warning.
Then what happened? A famine did come, and Paul was seized.
There are some theologians who labor to claim that Agabus erred, at least in the second case, but their real agenda seems to be to justify their churches' error-filled "prophecies." This false teaching of error-prophecies promotes the further proliferation of more false prophecies. We should not justify the "prophesying" that goes on in churches by reverse-engineering a doctrine that validates it.
God miraculously revealed to Peter that Ananias and Sapphira lied about their gift (Acts 5:3-10). Ananias and Sapphira indeed had lied about their gift, proven by their sudden deaths. This accuracy is consistent with Moses' teaching back in Deuteronomy 18:20-22. A "prophet" may claim to foreknow something from the Lord, but if it isn't true, they are a false prophet.
* My guess as to why the church responded so readily to Agabus' famine warning is that he must have been known to the brethren as a reliable minister. A stranger would not have commanded such a quick response.
In the strict sense, the office of New Testament prophet finished in the first century, because they along with the apostles received the new revelations of the faith (which was an indispensable element in being a prophet), and laid the foundations of the Christian faith (which is a finished work). But the spirit and power of godly prophecy lives on in the faithful preaching of God's pastors. These are six marks of a truly prophetic ministry:
It does not add to the Bible. It is judged by the Bible. It upholds the fundamentals of the Christian faith. It is animated by a spirit of Christian love. It comforts, encourages, and builds up the saints.
If some extraordinary guidance happens, it will always turn out to be doctrinally orthodox and factually true.