Preheat the oven to 190°C/375°F/gas mark 5. Line a twelve-cup standard muffin pan with paper liners/muffin cases.
Put the flaxseeds in a high-performance blending appliance and process into fine flour. Transfer to a large bowl. Add the whole wheat flour, cornmeal, coconut, baking soda, baking powder and sucanat (or brown sugar); stir with a dry whisk to combine. Stir in the water, maple syrup and lime juice. Mix just until incorporated.
Divide the mixture among the lined muffin cups. Bake for 24 to 27 minutes, or until golden and a toothpick inserted in the centre of a muffin comes out clean. Put the pan on a wire rack. Let cool for about 5 minutes.
Carefully remove the muffins from the pan and cool for about 10 minutes longer. Covered tightly and stored in the refrigerator, leftover muffins will keep for about 3 days.