In a medium skillet, heat oil over medium heat. Add garlic and red pepper flakes and cook until fragrant, about 30 seconds. Add kale and cook, stirring, until wilted, about 2 minutes. Add edamame and cook until heated through. Season with salt. Transfer to a bowl with rice and top with cabbage.
In a small pot, bring 2 inches water to a boil and reduce to a simmer. Crack egg into a teacup and gently slide into water. Cook until white is just set but yolk is still loose, 3 to 4 minutes. Remove with a slotted spoon and serve over rice and vegetables. Season with salt and red pepper flakes.