A flare is something we use to draw attention, or as a signal for help. As in, hey, my car is broken down over here—don't run into it! Or, hey airplane, I'm down here stranded on this island, please pick me up! We think our speaker definitely wants to call our attention to what she has to say. And that's a good way to start a poem—by catching our eye and drawing our attention to its message.
But "flare" can also mean an increase or outburst (maybe you've heard someone say that "tensions flared.") Specifically, this often refers to brightness, like the way our speaker uses the word in the first section of the poem: the sunrise "flaring all over the eastern sky" (1.4). We think this burst of light might also be what our speaker (and most poems) are going for: a flash of illumination, a brief insight.
And finally, there's the way our speaker connects the word to the sun. After all, there's this daily illumination of all the things in this world, and our speaker wants us to take note.