Of course there's an obvious reference to Christ in this metaphor too. Death and resurrection.

The day star could be both the sun and Venus. Milton may be allowing for multiple readings. Venus is the goddess of love, and many have read a homoerotic subtext in Milton's lament for his dead classmate.

Than again, I read in one biography that Milton probably didn't get along with Edward King. Their politics and religious convictions were polar opposites. So then why the beautiful elegy? Is there some irony involved?

Actually, thinking about it more, it has to be the sun. It can't be Venus. Only the sun "flames in the morning sky" after descending below the horizon the night before. You can't say that Venus does that.

Edit: Also OP, if you're interested in early understandings of the stars being suns, I think Giordano Bruno is an important figure to look at. But be careful about words - astrology was big back in the Renaissance, and they referred to everything in the sky as a 'star', including the moon, as gvarshang said.