And here's an example using the Blink project for anyone else who's interested.
1. In Impact, open up the 'PROM File Formatter' and configure as below (choose the output file name and location as you desire). Click OK.
2. Add the BIT file when prompted and Generate the PROM file (aka an MCS file).
3. Back in Impact, create a project with the Spartan 6 FPGA, and right-click to 'Add SPI/SPI Flash...'
4. Add the MCS file created in step 2 and click Open.
5. Select the correct SPI device in the drop-down list (S25FL032P) and click OK
6. Click on the green FLASH icon and select Program.
7. Choose options as below and click OK:
8. The flash is programmed (this can take a while)...
9. The Program Succeeded message should appear, and the code should be running (in my simple example, the LEDs are flashing). When the board is powered off and on, the FPGA will also be configured from the flash as desired.