I have been able to program an LPCXpress 55S28 board using Flash Magic through the UART, but unable to do so through USB1 (high speed).
I can see the USB interface appear in Flash Magic. I can read the signature. But I can't program it. The error is
LPC55S28 (USB, LPC5500) Operation Failed. (programming - failed to send data to the device)
I have tried it with both Flash Magic 13.50 and 13.61, both unsuccessful.
This person seems to have encountered this too, several years ago, without resolution:
LPC55S28 (USB, LPC5500) Operation failed
Another person has reported a similar error with LPC55S69:
LPC55S69 Not Programming through USB