Place an oven rack in the middle position. Preheat the oven to 350F (180C). Spray a 9-inch square nonstick pan with baking spray.
Place the flour, brown sugar, cocoa, granulated sugar, baking soda, and salt in the pan, and stir until completely combined. Make a large well in the middle of the dry mixture. Pour the oil, vinegar, and vanilla into the well.
Drizzle the water over the whole mixture then stir until completely combined. Wipe the inside edge of the pan to clean up any residual dry mixture.
Bake until just firm and a toothpick inserted into the center comes out with moist crumbs, 25 to 30 minutes. Immediately upon removing the cake from the oven, poke holes all over the top. You can use a fork, toothpick, chopstick, or cake tester to do this. Microwave half of the marshmallow fluff for 15 seconds. Then spread over the top of the cake. Place the cake to cool completely on a wire cooling rack.
Once the cake has completely cooled, spread the remaining fluff on top of the cake. Top with crushed graham crackers and chocolate chips.