This is a video of Youtuber The Action Lab producing a black fire that casts a shadow by exposing an alcohol flame to salt water that's all being illuminated by a low pressure sodium lamp that only emits light in a very tiny wavelength range of monochromatic yellow. *breathing heavy* It works because the sodium atoms being released from the salt water absorb the wavelength of yellow light from the lamp, making the fire appear black. Of course, using the scientific method, we also can't rule out the possibility of black magic. Which is of course 100% what this is, since it is a black flame and all. I've seen Hocus Pocus before.
Keep going for the video, actual black flame around 4:00.
Thanks to Damien, who agrees this would have been much more valuable information three years ago when I was an evil wizard for Halloween.