Rendering black fire doesn't work in Cycles

When it comes to volumetric emission, it’s better to think of colours as numbers.

For bright colours, the numbers are high and so your emission volume emits lots of light.

If you turn your colour to black, the numbers are zero, and so your emission is also zero. Zero emission volumes are transparent.

If you want part of your flame to appear black, you need to use volumetric absorption/scatter.

I haven’t tried it with volume emission - but for normal emission shaders, you can force cycles to emit negative light by making the emission value less than zero (e.g. -1). What will happen is that your object will appear black, and anywhere where this ‘negative light’ falls in your scene will appear darker too. It’s possible the same trick works with volumetric emission - maybe give it a try.