combustion - Can flames be colored black?

Most of us here would know that flames can be colored by adding an appropriate salt to the 'fuel' or by simply introducing it into a flame. Boron and Barium salts give the flame a green tinge, Strontium colors it red, Sodium does gold, copper a bluish-green, etc, etc.

Now from my (not-so-in-depth) high-schooler level of understanding, the energy released by whatever is being burnt to produce the flame in the first place (as is usually the case), excites electrons in metal ions in the salt to higher energy levels. And when these electrons 'de-excite' and drop back to the original energy levels, they emit that extra energy as photons (whose frequencies are determined by the Planck equation $E = h\nu$ ) and these photons are what we perceive as the colored flame.

If I'm not mistaken the book Harry Potter and the Philosopher's stone mentions a 'black flame' of sorts, being one of the obstacles Harry has to circumvent in order to reach the Stone. (Artist's depiction)

Now, as I understand it, for something to be 'black', it must absorb all ( or at least a fairly significant amount of) visible light, encompassing a wide range of frequencies.

Going back to colored flames, I mentioned that the ions must emit light energy, not absorb it, in order to color the flame.

Armed with all this information, would anyone know if it really is possible to create 'black colored flames'? Has it ever been achieved?

[I tried thinking it out myself.....just gave me a headache]

Edit 1: And yes, I've made note of what @Mithoron mentioned, but what I mentioned was just conventional logic, it isn't universal though.

...Newtonian mechanics was 'conventional logic', but we all saw how that failed in relativistic scenarios. So I didn't want to take the risk, hence I've asked If it actually is possible...

Edit 2: Just because someone mentioned otherwise in an answer... I emphasise that by black flames I don't mean invisible flames.

Answer

If black means that the flame does not emit light that is visible to the human eye then there is a certain chance that black flames might exist.

Since hot flames emit black body radiation and the spectrum of visible light reaches from about $\pu{400nm}$ to $\pu{800nm}$, a black flame had to be cool enough to not emit too high intensities of light below $\pu{800nm}$. So we're searching for a cool flame.

While cool flames are hardly visible in daylight, it might be difficult to find one that is invisible in a dark environment. Here is a report of a cool flame that could only made visible in the dark by long photographic lighting.