A source of radiation from black holes is stuff spiralling into the black hole, heating up as it "fell" and released its gravitational potential energy. Again this is black body radiation but this time the regular kind: the hotter the emitters are is the shorter the wavelength. This radiation comes from next to the black hole, not out of the hole itself.
The X-rays come from hot gas orbiting around the black hole in an
accretion disk. As the gas orbits, magnetic stresses cause it to lose
energy and angular momentum, thus spiralling slowly in towards the
black hole. The orbital energy is transformed into thermal energy,
heating up the gas to millions of degrees, so it then emits blackbody
radiation in the X-ray band.
Once the gas gets closer than a few times the horizon radius, it
plunges into the black hole, so while some X-rays can still escape
just before the horizon, most are emitted a fair bit outside.
Telescopes to detect black holes look for the most energetic rays, which are emitted from the hottest areas of gas nearest the hole. We cannot stand on a planet and look up and see xrays. But consider: if there is very hot gas, next to it there is less hot gas, and next to that gas that is less less hot. The cooler a blackbody is, the longer wavelength the emitted radiation is. Somewhere in that progressively cooler cloud is gas which emits radiation in the visible wavelength.
I here assert that the gradual change in temperature of this cloud as it is progressively farther from the hottest innermost gas should produce a gradual change in the frequencies emitted. The first visible light would be in the far violet, nearest the hole. This will grade through blues and greens farther away and then to red at the farthest coolest part of the cloud.
This prediction should be true not just for black holes, but for any cloud of gas heated from within. Now let me look... here we go.
The black hole rainbow cloud will be more symmetric than this one. The star is spewing this stuff out willy-nilly but the hole is sucking gas in, so it will be a symmetric spiral.