Once you have that working you will need to customize one of the example external Flash bootloaders. Choose the closest one. They can be found inside the Flash Magic installation and are all Keil uVision projects.
The S25F129P LPC18550/LPC4350 Hitex is possibly the closest. This uses a generic SPIFI library written by NXP. I don't know if your external flash part is supported or not.
You will need to modify this external bootloader project. In FlashPrg.c change DESCRIPTOR_BOOTSTRAP_BOOTROM to DESCRIPTOR_BOOTSTRAP_SWDLINK2. This sets the method for how the secondary (external flash) bootloader gets onto your LPC4370.
Check all the other settings in FlashPrg.c to make sure they make sense. Also change the name and description fields.
Compile.
Place the hex file of this secondary bootloader into the Flash Magic installation inside the Bootloaders folder.
Restart Flash Magic and you can now choose to select your secondary bootloader from the External Flash selection of the device database.
Also you can hire us to do all of this, along with testing, if you don't want to get this involved.
Andy