Preheat oven to 400°F (200°C).
Place the feta block in the center of a baking dish and surround it with cherry tomatoes.
Drizzle with olive oil, sprinkle with garlic, red pepper flakes, salt, and black pepper.
Bake for 25-30 minutes, until tomatoes burst and feta is soft.
Meanwhile, cook pasta according to package instructions; reserve 1/2 cup pasta water.
Remove dish from oven and mash the feta and tomatoes together to form a creamy sauce.
Stir in shredded chicken and cooked pasta, adding reserved pasta water if needed.
Top with fresh basil and serve warm.