Looks like this might be more of an STM question - and I'd need to use the FSMC to do it (along with changing a lot of the WICED MCU support code). Has anyone done anything similar?
This is an STM question and as far as I know most microcontrollers do not support running from external SPI flash due to the limited bandwidth. There are some microcontrollers that support quad-SPI flash memories which can run at impressive rates however that is not a standard embedded system design.
The STM32F4xx platform has support for the FSMC peripheral and we have an audio demonstration platform that utilizes it to communicate with external PSRAM. This can be found in WICED/platform/MCU/STM32F4xx/peripherals/platform_ext_memory.c.