Heat the oven to 375 degrees F. Squeeze the thawed spinach in a clean kitchen towel until completely dry.
In a large bowl, stir together the cream cheese, sour cream, heavy cream, garlic, onion powder, black pepper and red pepper flakes until smooth.
Fold in the spinach, 1 cup of the Monterey Jack, the feta and 1/4 cup of the Parmesan.
Spread the mixture in a greased 1-quart baking dish. Top with the remaining 1/2 cup Monterey Jack and 1/4 cup Parmesan.
Bake for 20 to 25 minutes, until bubbling at the edges and golden on top. Air fryer: use a 7-inch round pan and cook at 320 degrees F for 12 to 15 minutes.
Rest the dip for 5 minutes. Meanwhile, toss the flatbread with the olive oil, garlic powder and salt, and bake on a sheet pan for 8 to 10 minutes, flipping halfway (air fryer: 350 degrees F for 4 to 6 minutes).
Serve the dip hot with the crispy flatbread.