Preheat the oven to 350° F. Line an 8"x 8" baking dish with parchment paper, or spray with baking spray.
Combine the ground flaxseed with 3 tablespoons water, and stir. Set aside for 5 minutes.
In a large bowl, whisk together all purpose flour, almond flour, salt, baking powder, and baking soda.
In a separate, medium bowl, whisk together the flax mixture, non-dairy milk, oil, almond extract, vanilla extract, and 1/3 cup white sugar.
Add wet ingredients to the dry ingredients, and fold together until no dry spots remain.
Add about 1 cup of chopped apricots to the batter, and gently fold them in until they're evenly distributed.
Pour the batter into the prepared dish, and use a spatula to spread it evenly. Top with a layer of the sliced apricots, then sprinkle the sliced almonds evenly over the cake. Finally, sprinkle the turbinado sugar evenly over the cake.
Bake for 45-50 minutes, or until a toothpick inserted into the cake comes out cleanly.
Let cool completely before slicing and serving.