In "Fahrenheit 451", what major event coincides with Montag's escape and in what ways are the two related?

The major event is that the city is bombed and destroyed.  If you look back at the novel, you will see that Bradbury laces the novel with references to war and imagery of fighter jets screaming by.  This gives the reader the impression that war is imminent.  It also fulfills the idea that the society, so full of violence and ignorance in part because of a lack of books, is doomed and is destined to destroy itself.

Montag's escape is related to the war because now he - and the other book men - will have the chance to return to the city and help the society rise from the ashes, like a phoenix, which one of the book men references in an anecdote he tells.

Had the war not began, Montag would have had to stay exiled in the woods with the other book men. The stage, though, is now set for the men to return to the city and use the wisdom of literature to help start things over and, hopefully, learn from the mistakes that doomed the city in the first place.