At lot (most?) of the fire debris went to fill in the space between the "lakefront" and the Illinois Central tracks.
Northerly Island was built in the early 1920s, supposedly with a lot of fill from the downtown, near west and near south - where the fire raged. But you know that Northerly Island has been expanded many times! If you look at a satellite photo, you see a north-south straight line "barrier" in the pond? That's the sea-wall of the original Northerly Island - far to the west of the beach.
So anyway, an awful lot of Grant Park - where the original fire landfill was dumped - is a green roof. Over the largest underground parking structure in North America... So when they excavated that, where did they dump it? Northerly Island was being expanded... Who knows?
Some of the things I've found there definitely date back to the 1800s.
Also, if you'd like a souvenir from the Great Chicago Fire, head over the 12th Street beach any time there a big storm out of the north. The south corner will have an accumulation of stuff washed up from the lake (which is where they pushed all the debris). Terra cotta, bricks, glass, porcelain, etc.