For interfacing USB-Serial Device with external SPI flash, you need to develop a host side application to send commands and data to the SPI slave device (Flash).
We have an example host application (developed in Visual Studios) for Windows to do data transfers with the on-board SPI EEPROM.
You can use the example as a reference and change it to interface USB-Serial to SPI flash.
Te example can be found in the path: <USB-Serial installation directory>\USB-Serial SDK\examples\usbserialexample\spimaster
You need to understand the SPI timing of the Slave device (Flash) and can alter the example project accordingly.