Prelude: I do not know this part of the story you refer to.
The picture you display here, however, contradicts the idea of "black flame", because if there were a black flame, it should absorb the light, and attenuate the sight across it. There is little evidence, however, that one of the seven containers is source of a "black flame" as the background is (still) clearly visible, and the blur likely more a question of "out of focus".
As @ZOZ correctly indicated, "black flames" you / the story refer(s) to do not exist as such. The black of a flame occasionally seen often is result of incomplete combustion in shortage of oxygen. To provide an example, starting a Diesel engine may generate soot.
A third cent. Your "Going back to colored flames, the ions must emit light energy, not absorb it, in order to color the flame." needs a revision. True, ions present in the flame may emit light due to their de-excitation; similar to additive color mixing. To enlarge the picture, however, absorption may still occur -- similar to subtractive color mixing. This is element specific (Fraunhofer lines in the solar spectrum, for example) and is used in analytical chemistry atomic absorption spectroscopy, too. The likelihood of the two processes is different, however. Hence to be efficient, ASSAAS works on temperatures largely exceeding the ones provided by a normal fire, a candle, a medieval torch.