Preheat the oven to 350°F. Prepare an 8x8" pan by greasing an X into the bottom with margarine, lightly greasing around the edges, and then lining the pan (or at least the bottom of it) with parchment paper.
In a medium saucepan over low heat, melt the margarine, stirring occasionally. [Update: You can also melt the margarine in the microwave - takes about a minute - we just didn't have one.]
Meanwhile, whisk together the ground flaxseed and water in a small bowl with a fork.
When the margarine is melted, beat in the sugar for a minute or two. Then beat in the flaxeeed and water mixture and the vanilla until combined.
Combine the dry ingredients in a separate bowl. Stir dry mixture into wet in 2-3 batches to avoid clumps.
Spread the batter evenly into the prepared pan, using a spatula or bowl scraper to smooth out the top, and bake for 30-40 minutes. They are done when a toothpick stuck in the middle comes out clean. Be careful not to overbake.