Can someone recommend a handy inexpensive USB programmer for SPANSION S25FL064P flash memory?
It's a SPI flash memory so most decent SPI flash programmers should do. They can be found below 30 USD. If you have a decent micro controller development board already you can probably program and read this chip easily. For instance the Arduino platform has SPI libraries. The pin pitch is 1.3 mm so you should be able to attach to the chip without even desoldering it using decent grabber probes.
Have you beep tested the board to see if any test points or headers connect to the flash memory pins?
If you don't want to hack something together yourself, here's what seems to be a competent and cheap SPI programmer on ebay. Which is supposed to support you chip. Although it is more fun to solve it yourself, you'll see how easy it is and next time you run into an unsupported SPI flash memory you'll solve it without issues.
You shoudl use an SPI flash parallel port programmer. It is a simple and very accurate programmer using a single 74ls244 ic.
You can get it at: http://www.spiflash.org/