There are a couple of ways that you might approach this on the LPC4370...
First of all, if you develop and debug your application as an RAM image (avoiding the use of the SPIFI flash completely), you can then, at the final stages of development, wrap a binary version of the image with a header - which allows it to be programmed into SPIFI flash - but which the ROM bootloader of the chip will then automatically relocate to RAM at reset. This wrapping can be done using the "image_manger" utility provided as part of LPCScrypt (http://www.nxp.com/lpcscrypt). For more background information on this, see the section on "Boot process for parts without flash" in the LPC43xx User Manual.
Alternatively, you can build your image such that it contains code that will copy some (or even all) of the code from SPIFI flash into RAM as part of its initialisation routine. A starting point for information on how to approach this can be found for LPCXpresso IDE at:https://community.nxp.com/thread/389110
Or better still, I would recommend switching to the replacement MCUXpresso IDE product, and look at the MCUXpresso IDE v10.1 User Guide, chapter 14, "Memory Configuration and Linker Scripts". For more information on MCUXpresso IDE, visit : http://www.nxp.com/mcuxpresso/ide
Regards,
MCUXpresso IDE Support