I still have not found a way to flash the Radxa Zero 3W via USB. The Radxa support team has not been able to fix the issue either.
However, I have found a workaround that allows me to flash the eMMC via an alternative route with reasonable effort:
- Flash linux image onto SD card
- Boot Radxa Zero 3W from SD card
- Configure network
- Copy image to Radxa Zero 3W via SSH
- Flash image to eMMC using dd command:
$ sudo dd if=<image> of=/dev/mmcblk0
Afterwards you can remove the SD card and the Radxa Zero 3 should boot from eMMC.