The flame is Saint Peter. His role, with that of Saint James and Saint John, is to examine Dante on his assimilation of the three theological virtues. From here to the end of the canto is Dante's profession of faith.
Faith is the first of the three theological virtues.
Hope and love, the other two, are the subject of the next two cantos. Actually John outran Peter to the tomb on Easter morning and waited for Peter to enter first. Just so those singing rings, to different measures Dancing in swift circles and in slow, Enabled me to judge their wealth of joy. When it had stopped, that fire of blessedness Breathed out these words directly to my lady, Exactly as I have repeated them. But as this kingdom gained its citizens By the true faith, it is good for its glory 45 That he should have the chance to tell of it.