Place fennel and carrots in small roasting pan; drizzle with half of the oil and sprinkle with half each of the salt and pepper. Roast in 400°F oven for 25 minutes.
Meanwhile, using kitchen scissors, remove backbone from chicken. Cut chicken into 8 serving pieces.
In pie plate, combine flour and remaining salt and pepper. One at a time, evenly coat chicken pieces with flour mixture, shaking off excess.
In large skillet, heat remaining oil over medium-high heat; brown chicken all over, about 7 minutes. Transfer to plate and set aside. Skim fat from skillet. Pour ½ cup water into skillet, stirring to scrape up any brown bits. Set aside.
Stir tomatoes, onion, garlic and thyme into pan. Add chicken and any accumulated juices. Pour liquid in skillet over top. Roast, basting occasionally, until juices run clear when thighs are pierced, about 40 minutes.
Arrange vegetables then chicken on warmed serving platter. In small saucepan over low heat, warm pastis; ignite and pour over chicken. Let flames subside.