I asked for help a few days ago about "Configuring an FPGA via FX3 CYUSB3014". But it wasn't full answer. And my research was going on.
I found out that a FPGA (Artix-7 in my case) and a SPI Flash can not be programmed using only FX3 controller. It is imperative to use a serial-to-USB converter to connect to the standard FPGA chain. The version that is available in the manual "AN84868 Configuring an FPGA Over USB Using Cypress FX3" works only for configure an FPGA in the slave serial Configuration mode and debugging FPGA through USB. But not for flashing the ROM. There is a method, but I do not want to use it, because it describes a little (XAPP1188; "FPGA Configuration from SPI Flash Memory using a Microprocessor") Unfortunately.
I decided to connect a serial-to-USB converter like a FT2232 to JTAG chain and use a separate data stream USB 3.0 and a FPGA-SPI Flash configuration separately. It'll be the easiest variant.
My new question is:
Is it possible to connect USB 2.0 and USB 3.0 with different controllers to a same connector? Should I break the line of communication USB 2.0 signals (DN, DP) from the controller FX3 to the USB 3.0 connector to connect to this place the FTDI USB 2.0 controller signals?
No, it is not possible to split the USB lines coming from the FX3. You should have a separate USB port for accessing the USB-Serial Bridge .