If your trying to use the Flash programmer on a custom board then presumably you have created your own Flash programmer hardware to download to the FPGA, as the standard ones are specific to a particular Altera kit.
Regardless, if the Altera code is written to work with 16 bit Flash width only then it will not work.
One idea if you get really stuck, though it's a bit a nightmare, would be to create 2 flash programmer harwdware designs - one that connects to the lower 16 bits of the flash data bus, one that connects to the upper 16 bits. You would then have to create 2 flash programming files, one containing the least significant 16 bits of your flash data the other containg the ms 16 bits. You could then program the upper and lower halves of your 32 bit wide flash devices seperately.
The hardest part of this is creating the two flash files from the original one.... but it may be easier and cheaper than re-spinning your PCB.