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:
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.