Preheat oven to 350F/175C. Brush oil (any neutral kind works) onto the bottom and sides of a 8x8" square pan. Line with parchment paper, for easy removal, if desired. (The parchment paper is not necessary but makes lifting out of the pan easier.)
In a large bowl, add dry ingredients: glutinous rice flour, sugar, baking powder, salt. Whisk to combine. Add wet ingredients directly on top: eggs, coconut milk, oil, coconut extract. Whisk well, making sure there are no lumps.
Pour into greased, parchment-lined 8x8 pan. Evenly sprinkle coconut flakes on top.
Slide carefully in oven and bake until cake is golden and puffed with firm edges, about 45 minutes. The coconut flakes will form a crackly, golden-brown crust on top. Cool at room temperature, in pan, for 10 minutes. The cake will deflate slightly as it cools.
Carefully loosen the edges with a butter knife. Then lift the parchment paper sling and transfer cake to a cutting board. Cut into squares with a serrated knife. Enjoy warm or at room temperature. (The cake is easier to cut when cool.)