Is a flyback diode necessary for a small sg90 servo motor?
No diode is needed, but you should put both some bulk capacitance and high frequency bypass capacitance across the power leads.

Keep in mind that this is a "hobby servo" motor.  You are not driving the motor directly.  You are sending signals to a controller in the same package as the motor, and that controller drives the motor.  Therefore, you should try to provide reasonably clean power and clean signals, but your circuit isn't driving a motor.