Heat the oil in a well-seasoned wok or a heavy-duty 12-inch skillet over medium-high heat until shimmering hot. Add the shallots, garlic, and red pepper flakes; cook, stirring frequently, until the shallots start to soften but not brown, 1 to 2 minutes. Add the chicken and cook, stirring, until it's no longer pink and the shallots are beginning to brown, 2 to 3 minutes.

Add the fish sauce, lime juice, sugar, and 1/4 cup water. Cook, stirring frequently, until the chicken is just cooked through and the liquid reduces to a saucy consistency, 2 to 3 minutes. (If the sauce reduces before the chicken is cooked through, add water, 1 tablespoon at a time.) Remove from the heat, add the basil, and stir to wilt it.