Preheat oven to 350 degrees F (175 degrees C). Grease 24 muffin cups or line with paper muffin liners.
Place half of the figs in a blender; blend until smooth. Chop remaining figs with a sharp knife.
Beat eggs, applesauce, white sugar, and brown sugar together with an electric mixer in a bowl until frothy. Mix in flour, blended and chopped figs, flax meal, cinnamon, pumpkin pie spice, baking soda, and baking powder. Slowly add flour with mixer on low; fold in oats. Spoon batter into muffin cups.
Bake in preheated oven until tops spring back when lightly pressed, 20 to 25 minutes.