The phrase “Chinese fire drill” has been part of the American lexicon since the 50’s.
According to NPR. it continued a pattern that started in the ’40s of associating the word Chinese to anything negative or chaotic.
In the 50’s it was a game played by teenagers out on a night of joyriding. Stopped at a light, the students would jump out of their car, run around like crazy people and hop into the nearest door just before the light turned green. Anyone who failed to get back in was left behind.
In the 1960s, “Chinese fire drill” was also used to reference any accident scene of great confusion.
The US military has also used the word Chinese in a negative way.
A Chinese ace referred to a incompetent pilot. A Chinese landing was used to describe any bumpy touchdown.
You can read a further breakdown of the use of the word Chinese in NPR.