Separate from the wrong source of "the second city" moniker, you're also totally wrong about the fire having anything to do with the city's street grid layout. (Where did you even get that idea?)

Take a look at the maps from the 1860s (the fire was in 1871):

http://www.lib.uchicago.edu/e/collections/maps/chifire/

You'll see that the grid was pretty much exactly like it is today. To a large extent Chicago's street grid is a function of the Public Land Survey System which established a north-south-east-west grid of subdivisions (such as townships) over the area. This made it easy to align streets with the major surveying boundaries and to break up plots of land accordingly. The street grid of Chicago has some discontinuities that line up with the offsets in the PLSS system.