Implementing UART flow control in microcontroller
If the bluetooth module supports control flow, you should just enable it and then it will work automatically on the module's side. If not, tough luck - you can't use flow control.

On the micrcontroller side, you must handle RTS/CTS manually with GPIO (or perhaps some magic UART library will do it for you).

EDIT: Apparently your particular MCU Kinetis K20 supports flow control as part of the UART hardware, so you can have the MCU do it automatically in this case.

Another alternative might be to have the module echo each character sent back to the MCU. This makes everything slower but can perhaps be used as poor man's flow control.