Please read the User Manual -chapter 21
There you will find the details of ISP programming mode explanation.
If your application do not require the ISP, make sure PIO0_1 pin is not tied to low during power on.
Thanks. So, for programming the flash in LPC1313 is possible only through the UART interface and is not possible if we are using only the SWD port. Can you please confirm my understanding?
You can use the lpcxpresso command line flash programming tools to program your device over SWD (as well as directly in the GUI, of course)
IIRC, FlashMagic can also be used over SWD as well as UART - but you should double check.