https://patch.com/new-york/new-york-city/fdny-official-fired-after-controversial-training-exercise-video-report

I’ve had the FDNY at my school *retired teacher) and they did this exercise. The school is 80% Asian, Korean and Chinese. That’s who lives in the neighborhood where it’s located. There are students and teachers of ALL races, practically. Indian, Black, White, mixed, others.
The exercise has ZERO to do with Black slaves picking cotton. Besides, they didn’t pick cotton with their mouths! That’s not how people pick cotton! 
The firefighters work with whatever students he finds at the particular school that hosts the FDNY for their educational programs. The firefighters can be of any race and so can the students. This fireman should either be reinstated immediately or else the FDNY should cease going to schools altogether. Let the parents educate their own children on fire safety. Parents and teachers, if you play the fool by taking offense where none exists, it’s your and your child’s loss. It’s also one less task the FDNY must undertake so they can concentrate on putting out fires.

I agree with Seraphina -- you don't pick cotton with your mouth. So no, I DON'T see the significance.

And what does it matter if a White, Asian, or black person does this exercise? None of them have any living history of picking cotton. Not even great-grandparents!

What, it's supposed to give the black kid PTSD? Do blacks avoid cotton clothing as a sort of trans-generational, ancient, latent PTSD now?

Newsflash: the cινιℓ ωαr (and the end of slavery, cotton plantations, etc.) happened in 1865. Which is 160 years ago. No one has any personal connection or memories of that, not even through great-grandparents. It's about as remote as the building of the pyramids now. "ancient history" as they say. Time to move on!

As I said, Woke Idiocy!  It wasn’t as if only Black students did the exercise while students of other races, White in particular, sat back and laughed. The point of the exercise is to have your breathing obstructed while doing a relay race. The students first do it while holding the cotton in their hand, then with it in between their lips. Compare. It gives the idea without doing any harm, of how the presence of even a little smoke affects one’s breathing. That’s all. When done, the cotton balls are put in the trash. Your wife might want to try it in homeschool. 
Wokeness results in true loss of intelligence.