When flaps come out (1) lift and drag increase. (2)Increasing lift increases the instentanious turn rate. (3)The loss in speed kills your sustained turn rate.
Points 1 & 2 are correct. Point 3 should be clarified and is more complex then that generalized statement.
Sustained turn rate is function of excess-power (power-available minus power-required). There are 3 dynamic conditions to consider.
(1) Sustained turn at negative excess power (where power-required > power available). Staying in this envelope means you will bleed energy eventually to the point you stall which then results in "killing your sustained turn rate" because you've bled your speed to the point that you've exceeded the critical AoA of the wing to be able to produce the lift needed to keep flying. The degradation of sustained turn performance is a result of needing to relax your turn or pointing nose-low to regain energy to fly at a velocity at or below CLmax given the g-loading.
(2) Sustained turn at positive excess power (where power-required is < power available). Staying in this envelope means you will gain energy while in a sustained turn even with flaps deployed.
(3) Sustained turn at excess power = 0 (where power-required = power-available). This is the condition for the "best sustained turn" for an aircraft when a plane can hold a sustained turn indefinitely flaps deployed not withstanding.
Total drag as a result of g-loading (induced drag) in a turn + parasite drag determines the amount of power-required and which of the 3 dynamic conditions you're flying in.
Dropping flaps does not automatically mean you're in condition #1 above which leads to degraded sustained turn performance.
Tango, XO
412th FS Braunco Mustangs