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Cover chicken breasts with plastic wrap and pound to uniform thickness as needed. Pat chicken dry with paper towels and sprinkle with ¼ teaspoon salt and pepper.
Heat 1 tablespoon oil in Dutch oven over medium-high heat until shimmering. Add chicken skinned side down and cook until browned on 1 side, about 5 minutes. Transfer chicken to plate browned side up.
Add thyme sprigs, pepper flakes, if using, and 1 tablespoon oil to now-empty pot and cook over medium heat until fragrant, about 30 seconds. Stir in potatoes, radishes, water, and ¼ teaspoon salt and bring to boil. Place chicken browned side up on top of potato mixture. Reduce heat to medium-low, cover, and simmer until chicken registers 160 degrees, about 10 minutes.
Transfer chicken to plate, tent with aluminum foil, and let rest while finishing vegetables. Stir asparagus, peas, lemon zest, orange zest, and remaining ½ teaspoon salt into potato mixture. Cook, covered, until vegetables are tender, 7 to 10 minutes, stirring halfway through cooking. Remove from heat.
Discard thyme sprigs. Slice chicken on bias ½ inch thick. Place chicken browned side up on top of vegetables in pot, adding any accumulated chicken juices. Sprinkle with tarragon and drizzle with remaining 1 tablespoon oil. Serve.