What a wonderful essay prompt! I would suggest the theme of wealth amid corruption. Realize, though, saying that the story has a "similarity" between Gilded Age America and saying that the story is an "example" of Gilded Age America are a bit different. I would suggest the latter idea, actually. The time period fits: the late 19th Century. That IS the Gilded Age. Let's begin by looking at the Gilded Age as a whole and then see how The Devil in the White City fits the theme of corruption in wealth.
The Gilded Age is generally thought of as the time in American History in the late 19th century. There were lots and lots of workers (mostly immigrants) to participate in the rapid advancements in industrialization. Because the American government was lax on regulation at the time, the rich were able to get richer and richer while the poor did their dirty work. If something is "gilded" it means that it is something ordinary coated with a very thin layer of gold. The wealth of this age wasn't all that it seemed. It masked a lot of misery by the immigrant classes.
Probably the best quotation in support of the theme of wealth and corruption is said by Ray Baker:
What a human downfall after the magnificence and prodigality of the World's Fair which has so recently closed its doors! Heights of splendor, pride, exaltation in one month; depths of wretchedness, suffering, hunger, and cold in the next.
The goal of the World's Fair in Chicago was to outdo the last one: the one in France that revealed the Eiffel Tower. Errors all along the way, due to poor planning, cost more and more money. An area of swampland is chosen (not a good choice), architects are lured in (and then asked to "donate" their time), a natural disaster in the form of a storm collapses many of the structures already built (and more money is spent rebuilding them). The irony is, the Fair is actually a grand sight to behold. Why? Because it is the thin layer of gold covering all of the problems in its realization.
The "White City" of Chicago in itself, due only to the "gold lining" of the fair, seems grand. However, people who attended the fair from all over the world couldn't help noticing the stark contrast between the fair and the surrounding dirty and undeveloped countryside. It's like the fair declared a bright future while living its own lie revealed by its surroundings. Further, when the fair was over, the people of Chicago had only their dirty, muddy, poverty-stricken streets to go back to, ... now full of garbage from the fair-goers. Again, the stark contrast:
Heights of splendor, pride, exaltation in one month; depths of wretchedness, suffering, hunger, and cold in the next.