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Please refer to this documentation: http://www.cypress.com/file/46126/download
In the above application note, a PSoC 5LP acts as a Bootloader Host and updates the firmware on the target device using SPI interface like you requested. So in your case you need to write a firmware and replicate exactly what is happening in the application note with the linux processor as your Bootloader Host and PSoC 5LP as the target device. You just need to use the host side APIs.
To do this, please refer to the Bootloader System APIs present in PSoC Creator\4.2\PSoC Creator\cybootloaderutils
Thank you very much for this response - very helpful and much appreciated!