Where does FloorPlanner exactly stores the diagram created? Is it some kind of Web Storage? Is it possible to get that in Local storage like in local drive?
You can implement your app to store it wherever you want.
The new FloorPlannerTS sample, The Tudors, uses the Storage extension to support three different kinds of cloud storage plus localStorage. But note that localStorage is inherently limited, by definition.
But it’s most common to implement your web app to store models on your own server. You have a lot of flexibility there to do whatever you need.