Preheat oven to 375° F and spray muffin tins with non-stick pan spray.
Whisk together the flours, flax seed, baking powder, baking soda, salt, and sugar in a large bowl.
In a medium bowl, blend together the eggs, oil (or oil and butter), Greek yogurt, buttermilk, and vanilla.
Make a small well in the center of the dry ingredients and pour the blended liquid ingredients into the dry ingredients. Gently mix together just until moistened. There should still be streaks of flour visible.
Fold in the cherries and chocolate chips. Do not over mix.
Fill prepared muffin cups about 2/3 full with batter and top with a sprinkling of turbinado sugar if desired.
Bake at 375° F for 20 to 25 minutes until golden brown. Remove from muffin tins and cool on a wire rack. Serve warm.