Meanwhile, make pesto: In a food processor, blend half the broccoli, basil, and 1/2 cup oil until combined. Add chicken and cook until skin is crispy and chicken no longer pink, 10 to 12 minutes per side. Add cooked rice to skillet and stir until coated in chicken juices. Return chicken to skillet and add remaining broccoli. Dollop with broccoli pesto and sprinkle with red pepper flakes.