Paul’s exhortation to the Thessalonians not to quench the Spirit and not to despise prophecy raises the question of how the Spirit’s work, especially through prophecy, applies to us today. Usually, the two positions on this question are categorized as continuationists and cessationists. The names imply their respective positions, but a closer examination beyond labels helps us to have a more productive consideration of this matter.
The reason is that the arguments get complicated the deeper one dives into the debate, and Paul’s words in 1 Thess 5:19-22 are a good example. While there is variation in the continuationist argument, some continuationists acknowledge that prophecy in the modern sense is not infallible. Cessationists, if they use the term prophecy in a modern context, would agree. Given that Paul closely ties not despising prophecy with testing all things in 1 Thessalonians 5, both camps are in agreement with Paul’s exhortation.
What it often comes down to is how we define our terms and on what foundation we’re building. Vern Poythress offers a helpful way to conceive of the distinctions between types of prophecy and other extraordinary gifts of the Spirit. He begins by reminding us that the Lord Jesus Christ is the ultimate expression of the Spirit’s gifting, for he was endued with the Spirit without measure. As the Messiah, he is the perfect prophet, priest, and king, who exercises the Spirit’s gifting to its fullest extent. As God, he is the one who distributes the Spirit’s gifting.
As Paul writes to the Ephesians, “But grace was given to each one of us according to the measure of Christ's gift. 8 Therefore it says, ‘When he ascended on high he led a host of captives, and he gave gifts to men.’ … 11 And he gave the apostles, the prophets, the evangelists, the shepherds and teachers, 12 to equip the saints for the work of ministry, for building up the body of Christ” (Eph 4:7-8, 11-12 ESV). The gifts are Christ’s to give because he possesses them in their fullness, and so he is the ultimate expression of the Spirit’s gifting.
But because Christ is not stingy, he gives out of his abundance. As Paul notes in Ephesians 4, Christ gave the apostles and the prophets, who occupied a foundational role in the establishment of the Church and the completion of the Scriptures. Again, to the Ephesians Paul says, “So then you are no longer strangers and aliens, but you are fellow citizens with the saints and members of the household of God, 20built on the foundation of the apostles and prophets, Christ Jesus himself being the cornerstone, 21 in whom the whole structure, being joined together, grows into a holy temple in the Lord” (Eph 2:19-21 ESV). There are expressions of the Spirit’s gifting that are extraordinary because of their integral function in the establishment of the household of God. As Poythress notes, the work of the apostles and prophets is unrepeatable. You only build the foundation once.
There are, however, repeatable expressions of the Spirit’s gifting that are mentioned in Ephesians 4, namely evangelists, shepherds, and teachers. These are, in the Reformed tradition, offices of the church in its established sense. Thus, they are not a general expression of the Spirit’s gifting, but a specific expression for the governance of Christ’s church.
Finally, there is the most general expression of the Spirit’s gifting in the various ways in which believers are equipped to participate in the building up of the body of Christ. There are different yet overlapping lists of gifts in various letters of the New Testament that highlight the diversity of the Spirit’s gifting in the church.
In summary, there are levels of expression of the Spirit’s gifting that help us to talk about spiritual gifts with more clarity. Insofar as we all acknowledge that only Christ, the prophets, and the apostles expressed and express the prophetic gift infallibly, for example, then we can talk carefully about prophetic expressions in the context of the offices of the church and in the members in general.
Applying this to 1 Thess 5:19-22, it is clear that nobody should quench the operation of the Spirit, since the Spirit works in every believer. Specifically with respect to the prophetic expression of the Spirit’s gifting, it is also clear that nobody should despise Christ’s prophecies or the prophetic activity of the prophets and apostles, as received in the Scriptures of the Old and New Testaments. Furthermore, no one should despise the prophetic aspect of preaching, or the prophetic aspect of fellow believers declaring God’s word. We all, of course, test everything against the only infallible rule of faith and practice, the Scriptures. In sum, Paul’s words are very much relevant for us today, even if we believe that the extraordinary gift of prophecy ended after the apostolic era.
 The following summarizes Vern Poythress, “Modern Spiritual Gifts as Analogous to Apostolic Gifts: Affirming Extraordinary Works of the Spirit Within Cessationist Theology,” Journal of the Evangelical Theological Society 39.1 (1996): 73-4.