Preheat the oven to 350 degrees F.
Combine the almond flour, rice flour, baking soda and salt in a large bowl. Stir the sugars and oil together with a wooden spoon in another large bowl until the sugars dissolve. Add the egg, vanilla and milk and stir until well combined.
Using a wooden spoon, stir the flour mixture into the sugar mixture in batches until well combined. Stir in the chocolate chips and the dried cherries until thoroughly combined. Cover the batter with plastic wrap and refrigerate least 1 hour if you are in a rush or overnight for best results.
Line sheet pans with silicone mats or parchment paper. Scoop the dough into 1 1/4-inch balls using a 1-inch scooper or melon baller. Bake until the edges begin to brown, 12 to 13 minutes. Cool on a cooling rack 2 to 3 minutes then move cookies to a cooling rack.
Cook's note: Grapeseed oil is a clean oil with has little to no taste when it cooks. It burns at the slowest rate, which makes it a good choice for even browning.