read/write CFI compatible flash

Using a CPU is the easiest way of doing it IMHO. There is a CFI flash controller for Nios.

If the data transfer doesn't need to be fast, you can write a simple protocol in software and use PIOs to interface with your modules. As an example a single bit input to the CPU to signal that the module is ready, a parallel output from the CPU with the data, and an additional output to say the data is valid.

If you need faster transfers, you should have a look at Avalon Streams. You can add a SGDMA to your CPU that can read a block of memory and put it into the stream. The transfer flow can be controlled by your hardware through the ready signal.

Hope this helps!