Preheat the broiler. Heat the olive oil in a large ovenproof skillet over medium-high heat. Add the artichokes and cook, stirring occasionally, until tender and browned in spots, about 5 minutes. Add the garlic and red pepper flakes. Cook, stirring, until the garlic is soft, about 30 seconds.
Add the tomatoes, 1 cup water, 1 teaspoon salt and a few grinds of pepper to the skillet. Bring to a boil, then reduce to a simmer and cook, stirring occasionally, until the sauce thickens, about 10 minutes. Stir in the chicken and basil; season with salt.
Meanwhile, toast the focaccia in a toaster oven or under the broiler and let cool slightly; roughly chop to make coarse breadcrumbs. Sprinkle the crumbs over the chicken mixture and top with the mozzarella and parmesan.
Transfer the skillet to the broiler and cook until the breadcrumbs are browned and the cheese is bubbling, 3 to 5 minutes. Let cool, 5 minutes. Top with basil.