Preheat oven to 400°. In a large bowl, mix chicken, spinach, feta, yogurt, garlic, dill, parsley, and red pepper; season with kosher salt and black pepper.
Brush a thin layer of oil over bottom and sides of a 13" x 9" baking pan. Lay one sheet of phyllo in bottom of pan, pressing up sides. Brush with a thin layer of oil. Repeat 3 more times so there are 4 layers of phyllo. Spread chicken mixture over phyllo in an even layer. Top with a sheet of phyllo and brush with more oil. Repeat with remaining phyllo so that there are 4 layers on top of chicken mixture. Brush with oil; sprinkle with sea salt.
Bake casserole, covering with foil if edges darken too quickly, until phyllo is golden brown, 30 to 35 minutes. Let cool 10 minutes before slicing.
