Preheat your oven to 350°F (175°C). Grease or line a muffin tin.
In a large bowl, mix together the grated carrots, grated apples, and flaxseed meal.
Add the gluten-free flour, brown sugar, baking powder, baking soda, cinnamon, and salt. Stir to combine.
In another bowl, whisk together the vegetable oil and eggs. Pour this mixture into the dry ingredients and stir until just combined.
Divide the batter evenly among the muffin cups.
Bake for 20-25 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Let the muffins cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.