Coat 13x9" baking pan with spray. Melt butter in large skillet over high heat. Add onion and reduce heat to med.;cook 5 mins. Add chicken and cook 8 mins,until no longer pink. Add spinach,salt,pepper,nutmeg and red pepper flakes;cook 5 mins. Transfer to large bowl. Stir in cheeses,eggs and oregano.
Place 1/2 sheet of phyllo in bottom of pan. Coat with spray. Repeat with 7 more half sheets,coating each.Spread spinach mixture over the top. Repeat with remaining 8 half sheets. Cut top layer into 8 equal pieces.
Bake at 375 for 45 mins.,until top is brown. Recut to serve.