The Bible doesn't.
On the broader issue, indeed neither of the original leaders of the Reformation styled themselves prophets (from 19c onward, there were some offshoots of Protestantism like that, but we don't need to focus on them).
However, not only some foundational traditions but also the Christian Scripture itself was received by the Reformation from the Catholic Church. While not claiming prophetic powers, the leaders of the Reformation introduced to their flock a particular interpretation of some verses, and they explained away some other verses, and denied some teaching of the Church in the manner contrary to the Catholic and Orthodox doctrines, and so they most certainly established new traditions. For example, replacing sacramental priests with ministers, explaining some sacraments as mere manifestation of inner acts of faith, and doing away with other sacraments, the very teaching that Bible alone is sufficient for all spiritual matters, the multiplication of denominations -- all these are traditions introduced by the reformers.
14You, however, continue in the things you have learned and become convinced of, knowing from whom you have learned them,15and that from childhood you have known the sacred writings which are able to give you the wisdom that leads to salvation through faith which is in Christ Jesus.
16All Scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness;
17so that the man of God may be adequate, equipped for every good work.
Seems that the Bible states that it is inspired by God and is all you need to be equipped for teaching, righteousness, in fact every good work.