Combine the butter and the olive oil in a large skillet over medium heat. Stir in pesto, garlic, and tomatoes, and simmer until the tomatoes start to soften, about 2 minutes. Season with red pepper flakes and black pepper to taste.
Stir the shrimp into the sauce, and cook just until they turn pink, 3 to 5 minutes. Add the spinach, and stir until wilted, about 1 minute.