In a large bowl, combine the water and yeast and set aside for 5-10 minutes until yeast dissolves.
Meanwhile, in a small bowl, combine the flax and 3 tbsp. warm water, whisk, set aside, whisking every few minutes until flax thickens.
Divide the coconut milk: spoon out the solid milk and the white colored liquid from the top of the can. The lighter colored liquid you can pour out or use for a different recipe.
Add the sugar, salt, coconut milk and flax to the yeast, and stir well.
Slowly add the flour, one cup at a time, until combined.
Melt 2 tbsp. butter and mix it into the dough.
Spray a large bowl with coconut or another oil spray.
Place the dough onto a flat surface and knead for 2 minutes. Then place the dough into the prepared bowl, cover with a clean towel, and set aside to rise for 2 hours.
Heat the oven to 350 degrees.
Remove the dough from the bowl and place onto a floured surface. Roll out the dough to 1/4" thickness. Using a pizza cutter, slice the dough into 1-1.5" squares.
Place the beignets on baking pans covered with parchment paper, and bake for 12 minutes.
Remove the beignets from the oven. Melt the remaining 2 tbsp. butter brush the top of the beignets with the butter. Sprinkle the powdered sugar on top, and enjoy! Beignets will keep in a tightly covered container for 3 days.