Hi Jakob Berglund,
As you mentioned above, your board doesn't have the SWD or JTAG interface, however the USB port is available.
So you can follow the these steps to program the flash.
1. First, force the MCU enter the USB ISP by referring to the LPC reference manual, and the chip will be enumerated as a driver.

2. Double click the driver, you will find a bin file whose name is firmware, then copying a new application executable file to the driver after deletes the firmware file. After that, the chip is programmed by the new executable file.

Have a great day,
TIC
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