Preheat the oven to 375°F (190 °C) degrees. Lightly grease two baking sheets. Set aside.
Make the flax egg: In a small bowl, mix the ground flaxseed and water to make the flax egg. Let it thicken for about 15 minutes.
Make the cookie dough: In a large bowl, combine the coconut oil, sugars, vanilla, salt, and baking soda, beating until smooth and creamy.
Add in the flax egg and plant-based milk. Continue beating until smooth.
Mix in the flour, followed by the chocolate chips.
Roll 1-2 tablespoons of dough into a ball and place onto the cookie sheets, leaving a few inches between each cookie. For small cookies (1 1/2 inches [3.81 cm]) cookies, use 1 TBSP of cookie dough. For larger cookies (2 1/2 inches [6.35 cm]), use 2 TBSP of cookie dough.
Bake for 12-15 minutes, or until edges are starting to turn a chestnut brown and the tops are lightly golden.
Allow cookies to cool on the baking sheet for 5 minutes before transferring them to a cooling rack.