The television show Chicago Fire is not insensitive the victims of the Great Chicago Fire of 1871. It is not insensitive because the Great Chicago Fire of 1871, was started by a cow kicking of a lantern, and the television series Chicago Fire is a drama that explores the professional and personal lives of the firefighters and paramedics of the Chicago Fire Department. Therefore, the television show is not insensitive to the victims of the Great Chicago Fire of 1871.
No, it's not offensive because the plot of the TV show has absolutely nothing to do with what happened in 1871. If anything, the series is like a tribute the lives lost in Chicago because despite that fire Chicago grew to become one of the most important cities to the American economy.
I do not believe the Chicago Fire series is insensitive to the victims of the Great Chicago Fire. It's a series, a TV show, and it doesn't merit attention to the point that we question it's motives. The show is for telling a story. It's not meant to offend people. If you're not a fan, the best thing you can do is turn the show off, especially if you don't like it.
Considering events took place almost 150 years ago, i can't imagine anyone alive today who could be close enough to the event to be truly offended. As with all historical accounts the viewer must take into account the fact that the show is made for a wider audience and any references are done so with respect to the memories of anyone lost in the original tragedy.