I will break the thrones of the world, Astair,
and fling them at your feet;
The king is speaking figuratively, of course. He's not planning to literally chop up a throne and throw the pieces of wood or whatever at her feet. "Throne" in this case is a substitute word for "kingdom". (There's a literary term for that; it's called metonymy). And when he says he's going to break them, he means he will break their spirit (as if kingdoms had a spirit that could break).
As for flinging the pieces at her feet, I think he means that he will make the kings of the world beg her for mercy.
The narrator could have kept it simple: "I will conquer the kingdoms of the world for you, and I will make the kings come here and beg for mercy at your feet." But that wouldn't have been half as much fun.
Flame and banners and doom shall fly,
A banner can "fly" in the wind, but flames and doom—can they fly too? Probably not, but the image is certainly terrifying.
This king sounds like he's been through some serious battles. And he probably enjoyed them.
and my iron chariots rend the sky,
It appears that this king has flying chariots, too. Maybe he thinks he's Thor. According to Norse mythology, Thor had a chariot that was pulled through the skies by goats.
Do these chariots literaly "rend" (tear) the sky? Not likely. But if you've ever been caught in a thunderstorm, you know the sound of a sky being ripped apart.
Maybe that is how his chariots sound as they're flying through the air.
Whirlwind on whirlwind heaping high,
death and a deadly sleet.
Like a whirlwind, the King of Midian is making a huge pile of "death" and "deadly sleet."
Actually, I'm not sure what's going on here, but it sounds pretty bad. The King of Midian sounds hell bent on conquering the world, and I wouldn't want to be the poor soul who is standing in his way. So if he wants me to kiss the feet of Astair, I will.