To reverse a servo you cannot just switch the external red and black wires. At best you will just have a servo that doesn't work until you switch them back, at worst you will fry something on the board. To actually reverse the servo you need to open it up and reverse the leads to the motor, as well as the outer two leads on the potentiometer. On some servos this is easy, on others it's nearly impossible due to the servos construction. Either way you have to be pretty hand with a soldering iron. Never fear there are alternatives.
Besides the computer radio, there are also reversing Y cables, where it combines the functions of a Y cable and reverses (electronically) the signal going to one of the servos. If you don't have a computer radio and can't link the two flaps to one servo, this will most likely be your best bet.