In "By the Waters of Babylon," what is the chronological order of the Great Burning and Destruction?

I am not completely sure what you are asking
here.

Are you asking which of these events came first?  If
so, I do not believe that they are separate events.  I believe that these are both names
for the catastrophic war that destroyed New York City.  Here is the only place the word
"destruction" is used in the story:

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When gods war with gods, they use weapons we do
not know. It was fire falling out of the sky and a mist that poisoned. It was the time
of the Great Burning and the Destruction. They ran about like ants in the streets of
their city—poor gods, poor
gods!

There is nothing in
this passage to indicate that these things happened at different
times.

If you are asking when they happened compared to the
story, clearly they happened a very long time before the time in which John
lives.