The Question and Answer section for James and the Giant Peach is a great resource to ask questions, find answers, and discuss the novel.
In Chapter 5, James excitedly runs off with the bag and makes a plan to create the mixture in the kitchen, in secret from his aunts. In his rush to get to the kitchen unnoticed, James trips on the roots of the ancient peach tree and the bag...
At what point or chapter in the story are you referring to?
I do not recall this being explained. I imagine the furnature came through the same hole that James came in.