The metallic paint increases the reflection through the white. White, whether flat or gloss, is a relatively translucent color. Depending on how heavily you apply the white paint, it should only take a few coats.
Stikpusher's suggestion is also a good one. Flat whites contain a higher pigment load than gloss whites, and use different pigment(s). Titanium oxide is the primary pigment in both, but it comes in two forms, rutile and anatase (the mineral names) Rutile is subtranslucent, has very high internal and external reflectance. This helps give gloss white it's brilliance. Anatase is opaque and has a relatively lower external reflectance. A gloss white will only contain the rutile type of pigment, and possibly a hide-enhancing "colorless" pigment (in lower quality paints). Flat whites contain mostly the anatase form, and more of it by weight. They also usually contain hide-enhancing pigments and sometimes a flatting pigment (microsilica, usually). All this leads to a thicker, denser paint coating than you get with gloss white.
I hope you were taking notes; there's a short quiz at the end of class…