“Three Streams” is a phrase that has come to the fore in the last 10 years or so, especially amongst Anglicans in the ACNA and in continuing Anglican churches. The phrase is meant to suggest (a) that there are three historic “streams” within historic Christianity — the Catholic, the Evangelical, and the Charismatic — and (b) that Anglicanism embodies these in a distinct way that can serve the renewal of the Church.

Prof. Gillis Harp has suggested that the notion may have its origins in Lesslie Newbigin’s The Household of God (1953) or possibly an article by Richard Lovelace in Charisma magazine in 1984. Regardless, it was brought to prominence by the late Wheaton College professor Robert Webber in his wide corpus on “Ancient-Future” worship, sometimes called the Convergence Movement. In an article for ACNA’s newsletter Apostle, Trinity School for Ministry’s professor emeritus, the Rev’d Dr Les Farfield writes:

The genius of Anglicanism is that for five hundred years it has held in creative tension three different strands of Biblical Christianity. Those three streams are the Protestant, the Pentecostal/Holiness and the AngloCatholic [sic] movements.

I must say I find this a problematic argument from a historical perspective: How many Anglicans before the twentieth-century charismatic movement would have found recognizable the claim that the “Pentecostal/Holiness” stream is an integral part of Anglicanism?
Source: Three streams (but not the ones you’re thinking of) – Covenant