I need to update the firmware through UART. In the past I used "reliable update" from mcu-boot (KBOOT) in Kinetis MCU. The fw application will receive the new firmware codes, store it in dedicated place, and when reboot the bootloader will get the new fw from that location and flash it into the main flash.
I will suggest to check the ISP commands, the ROM code in the LPC MCUs can be used to update the firmware. The Flash Magic tool can be used to send this commands or you can check the structure in the 5.4 USART In-System Programming in the user guide.