I received a response from a member of Cypress Development Community, that's not very promising, but still ...
"We don't have any linux drivers for Encore II which can be used with flashrom utility. Please check with Nano USB if they have any driver to communicate with the programmer on Linux. Best Regards, Sananya"
Given the obvious close relationship (at least to me it seems so), between Cypress FX3 and EncCore II families of USB devices (name of Windows driver for Nano USB programmer, device name...), and considering the ongoing development of Linux SDK for FX3 series devices, I was hoping for a bit more optimistic response, but I guess I was wrong. I still believe that Nano USB programmer, as well as Cypress EnCore II CY7C63813-PXC have a great potential for flashrom community, but the lack of Linux driver is a definitive setback.
Kind regards, Bostjan