Preheat oven to 375 degrees F (190 degrees C). Line a muffin tin with paper liners.
Place walnuts in the bowl of a food processor; pulse until finely chopped.
Mix chopped walnuts and flax seeds in a large bowl. Mix in self-rising flour, butter, brown sugar, eggs, and milk until batter is smooth and no longer lumpy. Stir in cinnamon. Fill muffin liners 3/4 full with batter.
Bake in the preheated oven until muffins are golden brown and tops spring back when lightly pressed, 20 to 25 minutes. Cool in the tin for 5 minutes. Transfer to a rack to cool completely.
