Heat oil in a medium nonstick skillet over medium-high. Add onion, and cook, stirring occasionally, until tender, 2 minutes. Add spinach; cover and cook until wilted, 1 1/2 minutes. Remove pan from heat; stir in marinara sauce and chicken. Divide dough into 4 equal pieces. Roll each piece on a lightly floured surface into a 6-inch circle. Place one-fourth of the spinach mixture over half of each dough circle. Top each with one-fourth of the cheese. Fold dough over filling to form half-moons, crimping edges to seal. Coat calzones well with cooking spray. Place calzones in air fryer basket, and cook at 325°F until dough is golden brown, 12 minutes, turning calzones over after 8 minutes.