Heat cream and coconut extract in a skillet or wok over medium-high heat. Whisk curry paste and chicken broth together in a bowl; stir into cream mixture and bring to a simmer. Add chicken, cover, and cook just until chicken is no longer pink in the center, about 3 minutes.
Stir red pepper, green pepper, onion, fish sauce, sugar, garlic, and basil into the curry mixture. Replace cover; cook until vegetables are just cooked through, about 3 minutes more. Stir in flour to thicken to desired consistency.