Hi, Fernando,
I have searched the "black magic probe" device, it is from ST company, and is used to download/debug for STM32 family, but i am not familiar with the device.
If you can use it to download/debug the LPC4320, I think it is okay.
As you know that the LPC4320 does not have on-chip flash, I suppose that you use external spifi flash and you want to download code to external spifi flash. Can you tell us the tools and the P/N of the external spifi flasg you are using to download to external spifi flash? if you use MCUXpresso tools, pls refer to section 15.2.2 LPC SPIFI QSPI Flash Drivers in MCUXpresso_IDE_User_guide.pdf, located at:
C:\nxp\MCUXpressoIDE_11.1.1_3241
I copy the part here:

Regard
XiangJun rong