Manx

I haven't yet been able to collect the resources necessary to reproduce the environment. But if you would like to make a donation, please let me know. So I can't tell you for certain. I have attempted to model it in Alias Wavefront's Studio 3D modeling software. It crashed during the render (go figure!)

For some strange reason, I have been thinking about this question for over a decade. Don't ask me why.

My conclusion:

You will see a field of brown-ish color.

I came to this conclusion based on my understanding of incandescent light. Essentially, what will happen is, the waves of light will spread out from the source and bounce off the mirror in an infinite number of directions, which will again bounce off the mirror in an infinite number of directions, and again - slowly bouncing fewer and fewer times due to the lack of energy in the flash light (i.e. after a certain distance, a light wave will become weaker and weaker, not because the power source in the flash light runs out). While the light waves are bouncing around the mirror in an infinite number of directions, they are also bouncing off of you and the flash light. Since each person is an assortment of varying colors, the end result is that those colors will all wash together as they are bounced around and around in an infinite number of directions. It becomes an additive color source due to the body (clothing, skin, hair, flashlight) absorbing portions of the spectrum.

Result: brown.

If you were wearing primarily red, the brown would be warm in tone. If you were wearing blue, cool in tone.

I'm open to alternative theories.