In a large bowl, combine the melted butter, minced garlic, Parmesan cheese, Italian seasoning, salt, black pepper, and red pepper flakes. Mix well to create a garlic-Parmesan sauce.
Place the halved baby potatoes in the bottom of the slow cooker. Pour half of the garlic-Parmesan sauce over the potatoes and toss to coat.
Arrange the chicken thighs on top of the potatoes. Pour the remaining garlic-Parmesan sauce over the chicken, ensuring it is well coated.
Cover the slow cooker and cook on low for 6-7 hours or on high for 3-4 hours, until the chicken is cooked through and tender.
Once cooked, carefully remove the chicken and potatoes from the slow cooker. Garnish with fresh parsley before serving.