Sift the flour, sugar, baking powder, baking soda, cinnamon, and salt into a medium bowl.
Cut the cold butter into ½-tablespoon chunks and add to the dry ingredients. Using a pastry blender or two forks, cut it in until pea-sized.
Add the buttermilk and almond extract; stir into a rough dough. Gently fold in the chopped peaches without mashing them.
Turn the dough out onto a floured surface, divide in half, and pat each half into a circle no more than ¾ inch thick.
Score each circle into wedges and transfer carefully to a greased air fryer basket.
Air fry at 350°F for 12–15 minutes, until golden and cooked through.
Whisk together the powdered sugar, almond extract, and cream until pourable. Drizzle over the cooled scones and let set.