There is an inseparable relationship between the spirit of prophecy and the testimony of Jesus Christ. This doctrine is most classically found in Rev 19:10, where John tells us, the testimony of Jesus is the spirit of prophecy. Joseph Smith loved to refer to this passage because people so often were critical of the claim that he was a prophet.
Joseph Smith
"Many of the sects cry out, 'Oh, I have the testimony of Jesus; I have the spirit of God: but away with Joe Smith; he says he is a prophet; but there are to be no prophets or revelators in the last days.' Stop, sir! The Revelator says that the testimony of Jesus is the spirit of prophecy; so by your own mouth you are condemned." (The Teachings of Joseph Smith, by Dahl and Cannon, p. 662)
Joseph Smith
"If any person should ask me if I were a prophet, I should not deny it, as that would give me the lie; for, according to John, the testimony of Jesus is the spirit of prophecy; therefore, if I profess to be a witness or teacher, and have not the spirit of prophecy, which is the testimony of Jesus, I must be a false witness; but if I be a true teacher and witness, I must possess the spirit of prophecy, and that constitutes a prophet; and any man who says he is a teacher or a preacher of righteousness, and denies the spirit of prophecy, is a liar, and the truth is not in him; and by this key false teachers and imposters may be detected." (History of The Church, 5:215-16)
Alma had taught by this same spirit of prophecy. By the power of the spirit of prophecy and revelation, Alma is able to teach doctrines which were later taught in the New Testament. That these doctrines were revealed to him before they were revealed to Paul or John the Revelator should not surprise for they came through the spirit of prophecy. It is interesting to note that in the end of Alma 5, he speaks of the spirit of prophecy (Alma 5:47), then immediately gives his personal testimony of Jesus Christ (v. 48).
From the above, we learn that every member of the church should have the spirit of prophecy because every member of the church should have the testimony of Jesus. As Joseph Smith said, "a true teacher and witness…must possess the spirit of prophecy." This is true for every teacher and witness in the Lord's kingdom.
Joseph Fielding Smith
"The Prophet Joseph Smith has said that every member of the Church should be a prophet, meaning, of course, that he should have that testimony of Jesus and keep himself in perfect accord with the Spirit of the Lord so that he could recognize truth and the Lord could reveal the truth to him, so that he might comprehend it. Every man in the Church has the right to receive revelation for his own guidance, but not for the guidance of the Church." (Conference Report, Oct. 1943, p. 97)