In a large bowl, combine flour, flax seed, baking powder, baking soda, and salt. Stir well.
In a Vitamix blender, blend oranges until smooth. Add applesauce, honey, oil, and vanilla. Blend on low until mixed well. Pour the wet ingredients into the dry. Stir just until blended.
Fold in cranberries.
Lightly spray muffin pan with olive oil cooking spray or use muffin cups. Scoop about 1/4 cup of batter into each cup.
Bake for 18 to 20 minutes or until the tops of the muffins spring back when lightly touched.