Hi,
when your DSP programs the SPI Flash, you have to hold the FPGA in Reset, by pulling the Prog_B line Low.
The DSP definitely needs to tristate the SPI Bus during FPGA boot and FPGA access.
I assume you need different FPGA configurations, because you want to program it from DSP? If not, it is enough to programm the SPI Flash one time with a JTAG adapter.
If you need only a few, please read the Spartan-6 Configuration User Guide for Multiboot.
best regards
Thorsten Trenz