There are direct USB-SPI chips available, so using PSoC can be avoided.
The KitProg2 ob-board programmer/debugger (PSoC 5LP device) present on most of the Cypress Development Kits supports USB-SPI communication. Have a look at USB-SPI Bridge section of the KitProg2 User Guide for some insight.
Also check out another USB Serial chip (CY7C6521x family) which can be used as USB/SPI Bridge.
I could not find a finished example of LabVIEW with CYUSB.dll
You can try to create a wrapper for your project.
I did a primitive wrapper for cyusbserial.dll and CY7C65211 (PSoC® 4 CY8CKIT-049 4xxx Prototyping Kits)
You can see it here: http://mylab.wmsite.ru/moi-razrab/cy7c65211/
Thank you for reply, but I don't want to add IC chips, because I already had manufactured circuit board.
Thank you for meaningful info.
I’ll try to start from reading this guide!