I think a couple things go into this. First, I’d expect the primary properties of the material to affect the sound of the flute would be its rigidity, elasticity, and density. Accoustic energy loss in the flute material will affect the higher frequencies more, resulting in a less bright sound. This might all be able to be folded into a single parameter, fall-off of the higher frequncy amplitudes.
Malleable metals like copper, tin, lead, and also pure gold likely would have reduced amplitudes of the higher overtones. An alloy of copper like brass (copper + zinc), however, is much more rigid. Iron would rust, copper and tin would corrode. Has anyone said glass, ceramic, or granite flutes would sound bad? I’d suspect that concrete (mentioned in the other thread) would sound OK, but taste nasty.
I agree that when you get into brass versus gold (alloy) or silver, the cost and status of the material probably does start to play into it more than the intrinsic material properties. However, if you’re a flute maker, why not use more expensive materials in the flutes you put more effort into? As the cost of makling the flute rises, the material cost becomes less important in terms of added cost, and more important in terms of status (i.e. marketing). This can be true for wood also. So “more expensive materials make a better flute” may be partially a self-fulfilling statement, but that doesn’t make it not true.