Hi, Richard,
Can you tell us the part number you are using?
Assume that you use LPC5569, so pls refer to the UM11126.pdf
Pls refer to section 34.7.5.1 Hardware flow control

As the above figure, the RTS signal is an output signal driven by receiver. The RTS is configured to appear on a device pin so that it can be sent to an external device, it indicates to an external device the ability of the receiver to receive more data.
Unfortunately, we have not the code to demo the RTS function.
Hope it can help you
BR
XiangJun Rong