Preheat oven to 425 degrees F. Grease 4 round ramekins with cooking spray and place on a baking sheet, set aside.
Set a saucepan over medium heat with the butter. Once melted, whisk in the flour and cook for about 30 seconds. Whisk in the milk and cook, stirring often, until the sauce has thickened. Season with a pinch of salt and pepper. Remove from the heat and set aside to cool slightly.
In a large bowl, whisk together the spinach artichoke dip, eggs, the cooled milk sauce, Monterey jack cheese, Romano cheese, garlic, pepper flakes and hot sauce until well combined.
Unwrap the puff pastry and cut the sheet into four squares. Place a square in each ramekin, pressing it down onto the bottom and up the sides of each ramekin. Divide the soufflé mixture between the ramekins.
Bake until puffed up and deep golden brown, about 25 to 30 minutes. Remove from the oven and let cool slightly before serving.