I don't know if there are parallel chips that work as stand-alone with FPGA. Otherwise, you do need another chip, like a counter, that feed an address to the flash, and increment on CCLK.
I know that if you have a serial flash, you can program it externally, even if FPGA is in-service. This require an extra bus buffer. Maybe something similar can be done for other flash type.
In any case, I don't see how to program the flash or mcu directly via RS232. You can however program the flash by using the mcu to do so, while giving the code over RS232. Most likely, the programming will take place using parallel port interface. If you design a JTAG and Program interface as standard used by that FPGA vendor, then you may also be able to program those using their software. Otherwise, you're free to build any hardware interface, as long as you write the software to interface it.