Pat chicken dry with paper towels and season all over with salt, pepper, and half of the cayenne pepper.
Heat a drizzle of olive oil in a large pan over medium-high heat. Add kale and a splash of water. Cook until kale is wilted and very tender, about 4-5 minutes. Stir in garlic and cook until fragrant about 30 seconds. Season with salt and pepper. Transfer to a plate.
Heat another drizzle of olive oil in pan used for kale over medium-high heat. Add chicken and cook, stirring occasionally, until browned and cooked through, about 4-6 minutes.
Return kale to pan with chicken and reduce to medium low heat. Add coconut milk. Stir in cream cheese. Bring to a simmer and cook until sauce starts to thicken and combine, about 2-3 minutes.
Add spiralized zucchini to pan with sauce and toss to combine. Cook until zucchini is heated through and the texture of noodles. Season with salt and pepper.
Divide between bowls, top with Parmesan if desired, and serve.