Pat chicken dry with paper towels. Sprinkle with ½ teaspoon salt and pepper. Heat oil in a 12-inch skillet over medium-high heat until just smoking. Add chicken and cook until golden brown on one side, about 4 to 6 minutes. Transfer to a plate.
Add onion and remaining ½ teaspoon salt to the skillet. Cook until softened, about 5 minutes. Stir in rice, garlic, and red pepper flakes, cooking until fragrant (about 30 seconds). Add carrots and stir to coat, scraping up browned bits from the skillet.
Nestle chicken, browned side up, into the skillet with the rice mixture. Pour in chicken broth and bring to a simmer. Reduce heat to medium-low, cover, and simmer gently until chicken reaches an internal temperature of 160°F, about 10 minutes.
Transfer chicken to a cutting board and tent loosely with aluminum foil. Stir the rice mixture to recombine, cover, and cook for an additional 5 to 10 minutes until liquid is absorbed and rice is tender.
Turn off the heat, sprinkle peas over the rice, cover, and let warm through for about 2 minutes. Add lemon juice and gently fluff the rice mixture with a fork. Slice chicken into ½-inch-thick pieces, arrange on top of the rice, and garnish with parsley before serving.