It's not meaningful to say what's "best for the flats", it's more what color is best for you.
Reds enhance contrast (amber, copper, etc)
Greys provide highest true color recognition (my choice)
Browse through any RGB color channel description (Adobe Photoshop manual for instance) to see how each color really influences what is emphasized. Colored sunglasses are color filters in essence.
If you see fish better by contrast, go reds. If you use more color recognition as I do, go grey. I also don't see reds well when wearing reds, thus am more prone to miss traffic lights etc. Not a good idea.
I prefer the true color and glare reduction combination over the false tones of amber and copper lenses. I don't need the contrast as much in the way I process what my eyes tell me in the brain, and the color is of very high value to me in elimination of objects which is just as important as positive identification.
It's most important to understand how your brain processes what your eyes receive in order to decide which tones work best for you, IMHO.