Preheat the oven to 350 degrees and line a 7x11 pan with parchment paper.
In a small bowl, whisk together the ground flaxseed and water. Set aside to thicken.
In a large bowl, whisk together the melted vegan butter, granulated sugar and brown sugar. Add the flaxseed mixture and pure vanilla extract and whisk until combined.
Add the all-purpose flour and cocoa powder to the bowl and stir until combined. Be careful not to over-mix. Fold in the chocolate chips and chopped walnuts.
Scoop the batter into the pan and smooth the top with a spatula. Bake for 40-45 minutes or until a toothpick inserted into the center comes out clean. Let cool throughly before removing from pan and slicing.