For the cookies, whisk together flour, almond flour, flax, baking powder, starch, and salt in a medium bowl. In a larger bowl, mix coconut milk, maple syrup, and coconut sugar with an electric mixer until light and fluffy. Beat in the vanilla and maple extracts until combined.
Beat in flour mixture in several additions, until just blended. Divide dough into two balls and flatten each ball into a disk. Wrap each disk in plastic wrap and chill 30 minutes to 1 hour.
Preheat oven to 350 degrees F (180 C) and line baking sheets with parchment paper or use a silicone baking pads. Roll out one disk of dough on a lightly floured surface until it is about 1/3 inch thick. Cut out cookies with leaf shaped cookie cutters dipped lightly in flour. Place cookies on prepared sheets about 1 inch apart.
Bake cookies until edges just start to brown, 8-10 minutes. Watch them closely as they can start to burn quickly. Cool cookies on sheets for a few minutes and then transfer to wire racks to cool completely.