Preheat your oven to 425 degrees F (232 degrees C). Spray a cast-iron skillet with cooking spray (or grease it with vegetable or canola oil). If you don't have a cast-iron skillet (Though, really, why don't you? They're awesome - cheap, heavy, naturally nonstick if you use them enough and take care of them. Go get one.), you can use an 8-inch square baking dish.
Bring the water to a boil in a small saucepan over high heat. Add the flaxseed, reduce to a simmer, and stir for three minutes, until you have a weird, gummy, smooth mass of stuff. It looks kind of gross - don't worry. Set aside.
Stir together the flour, cornmeal, sugar, baking powder, and salt in a medium mixing bowl.
Add the soymilk, oil, and flaxseed gunk to the dry ingredients. Stir until just combined - don't over mix.
Put everything in the skillet. Bake for around 20 minutes, until a toothpick inserted in the center comes out clean.
Let the cornbread cool in the pan for a few minutes, then remove it from the pan and let it cool on a wire rack for around ten minutes.
Don't overmix the batter.
Allow it to cool for 5-10 minutes before slicing so it's easier to serve.
Don't make your oven too hot. This can result in dry cornbread.
Go ahead and add some fresh corn or a can of diced chile to this recipe, if that's your thing.