Chances are what is "flaking" off is soap residue, which is also what is being discolored. As Brownie said, if the sink and top appear to be one piece, with no noticeable seam between the two then the sink is also Corian. Using a scot brite pad lightly sand the entire sink (and top if needed). This will take off any residue and renew the sink/top to original finish. It will also remove small scratches.
Corian is acrylic resin with ATH filler.
2011 Toyota Tundra double cab