The smoke in the latter parts of this film were more likely from steam engines in the railyards just to the west of Soldier's Field. Hydrogen burns very quickly, with almost no visible flame and even the burning remnants of the envelope would not produce that amount of smoke.
Settles was a highly accomplished, Naval Aviator. He was acting as pilot for Jean Piccard for a high altitude balloon from Chicago in 1933. Here is the link to the Wikipedia article about the flight:
http://en.wikipedia.org/wiki/Thomas_G._W._Settle
If I'm not mistaken, the gondola from that flight is still (or, at least was, when I was a kid) on display at Chicago's "Museum of Science and Industry."