Well first I'm going to assume that you are fishing for Tarpon, Bones and Permit with a few Barracuda, Jacks and more mixed in. I list Tarpon first as many hit the keys around May keying on those big silvers that go a bit gaga when the worms hatch. The flats are a mixed lot, from lots of sand, to good grass flats and some with a good bit of marl or muck bottoms here and there. Weather is usually sunny for the most part although a storm or two can roll through. The time between around 9am till around 3:30pm is the prime time as the sun's angle is superb then for using the polarization of your glasses. When the sun drops below 37 degrees morning or night the effective polarization drops off quickly. That said I like you evidently, liek something along for the mornings and evenings as well as overcast days to boost contrast, add a bit of shading, add polarization, etc. My choice were a pair of ultra light wrap around Hobies in the lightests yellow imaginable. These are the only glasses I use that do not have a glass lens. As good as the plastics are the can't compare to glass for clarity and sturdiness. The wrap around also helps block all side and overhead, under reflections that will destroy your ability to ferret out a fish among the sand patches.
For midday, my choice is the darker brown, http://www.sporteyes.com/smithcolors.htm and if you notice they offer the lowest percentage of passed light even better than the coppers. Were I fishing over strictly grass, I might go to my greens as they do boost contrast when there's a bit of green to contend with. Both my Browns and Greens are AO (Smiths) with the glass lens and I do use side shields and wear a wide brimmed hat that has the underside of the brim blackened. I mentioned the Tarpon and other fish above as the predominate side color of these fish is silver and highly reflective of the bottom. I've had great luck with many brands of sun glasses but these days stick to the AOs, Hobies, Costas, Haber, etc (top quality) Oh yes, on that side reflection, as you will depend on contrast a lot to see the outline of back and belly of the fish as well as any bars or shading. The yellow or yellow component of brown and even the greens is what boosts that the most. Check out my blog for a good bit more on what makes good flats glasses and add to that list given above a good pair of lightweight binos a great aid in finding birds and the fish they follow.