Which board is it and what flash is it using? If it is a parallel flash, you should be able to upload a parallel flash loader (http://www.altera.com/literature/ug/ug_pfl.pdf) image into the FPGA using the Quartus programmer, and then if you do a new autodetect, it should show you the flash with options to read/write/erase it. I don't use parallel flashes myself so I don't know the exact procedure, I just know it is possible.
If it is a serial flash you may have a special connector on the board to connect the USB blaster directly to it, and then you should also see it in the Quartus programmer when doing an autodetect. Without the special connector you must use the serial flash loader (
http://www.altera.com/literature/an/an370.pdf). Even if you just need to read back the flash contents, you will have to create an empty project with the correct FPGA and EPCS flash, generate a .jic file from that and use it with the serial flash loader in the Quartus programmer to read back the flash contents.
By the way, the read function in Quartus programmer is called "examine".