In theory maybe you could build a version made of inks printed on a reflective mirror? And then you would hold the mirror so it reflected the object into the camera?

But that seems far more difficult. Precisely combining and applying combinations of inks to a mirrored surface sounds like a helluva manufacturing challenge.

I think ink and mirrors are kind of fundamentally incompatible.

Probably closer to what you're thinking about would be putting a bunch of tiny bandpass filters infront of a mirror, but in that case you can ditch the mirror entirely and just point the camera through the filter array.

A filter array right on-top of the sensor is how (the vast majority) of) CMOS cameras distinguish colour anyway.