Season the chicken breasts on both sides with salt and pepper. Lightly grease the grates of an outdoor grill. Heat the grill to medium-high heat.
Grill the chicken breast turning at least once for about 10 minutes per side or until the chicken is fully cooked (the internal temperature has reached 165 Degrees F). When the chicken has cooled enough to handle, slice it into thin strips.
Chop the canned artichokes. In a small saucepan melt butter over medium heat. Add the shallots and garlic. Season with salt and pepper. Cook for about 5 minutes until tender.
Add the artichokes and cook for 3-5 minutes. Add the cream cheese and reduce the heat to medium-low. Cook the mixture until the cream cheese melts and can be stirred easily. Add the spinach and cook for another minute just to heat through.
Preheat the oven to 425 degrees F.
Top the flatbreads with a layer of the cream cheese spread, followed by even amounts of mozzarella and parmesan cheese and top with the grilled chicken.
Place into the oven and bake for 8 minutes or until the flatbread is crisp and the cheese has melted. Top with additional parmesan and chopped spinach if desired.