Preheat the oven to 350 degrees F (175 degrees C). Line 24 muffin cups with paper liners.
Blend 1/2 of the figs in a blender until smooth. Chop remaining figs with a sharp knife.
Beat eggs, applesauce, and sugars in a large bowl with an electric mixer until frothy. Mix in blended and chopped figs, flaxseed meal, cinnamon, pumpkin pie spice, baking soda, and baking powder. Slowly add flour with the mixer on low, then fold in oats until incorporated. Spoon batter into the prepared muffin cups.
Bake in the preheated oven until the tops spring back when lightly pressed, 20 to 25 minutes.