The idea that everyone can be a prophet is central to all of our ancient scripture .
1) The Bible Dictionary indicates (and Joseph Smith taught) that prophecy is anything that comes from God, especially through the influence of the Holy Ghost.
2) Many Old Testament prophets came from nowhere and suddenly were preaching to the people and the kings. Lehi is a great example of someone who had a vision and preached to the people of Jerusalem - who probably rejected him just as much for his lack of institutional standing as for his doom and gloom, repent or be destroyed message. Samuel, the Lamanite: How was he called?
3) When there is an established "church" (New Testament and Doctrine & Covenants, for example), "prophet" seems to become seen as a position or calling; when there is not such a "church", prophet is a description of one's activities and words.
4) Prophet isn't an official position or office in the LDS Church (like apostle is) - and I think that strengthens my point that all of us can be prophets, at least in some way and to some degree.