Preheat oven to 350 °F (175 °C). Line a 12-cup cupcake pan with liners.
Mix the flax seed and water together in a small bowl, and allow to sit for ~5 minutes. If you have store-bought egg replacer, you can use it instead.
In a large bowl, mix all the dry ingredients (flour, baking powder, baking soda, salt, green tea powder) and whisk together. Set aside.
In a separate bowl, mix all the wet ingredients (sugar, oil, non-dairy milk, vinegar, vanilla extract, flax seed mixture).
Add the wet ingredients to the dry ingredients, and mix until about incorporated.
Fill each cupcake liner 3/4 full. Bake for 18 minutes until the cupcake springs back, or until a toothpick inserted comes out clean/with a few crumbs.