When there's multiple flickering LEDs in the same room, they create interference. So even if we don't notice a single one flickering, when all of them go from black to full at the same time, and this happens 20x a second, we can notice that.
In general, light is linear and time invariant. That means in a flickering light system, a flicker of blue light then of red light, or red and blue at the same time, are indistinguishable if the 'sampling' system doesn't have sufficient bandwidth to resolve the flicker at all.
There do exist nonlinear optical components[1], but none that exhibit nonlinearities at the light intensities you'll find at home!
Additionally, even if the above were not true, flickering LED sources tend to flicker at a multiple of the AC supply, so it's very unlikely you'd see one flickering at 1000 Hz and another at 1001 Hz for example. For battery powered devices, it could easily happen though.
https://en.wikipedia.org/wiki/Beat_(acoustics)
I don't see why the same effect would not happen with the light sources.