Yes. Those types of clips. It works fine with the Tek and old HP clips that I have, except the flat hp logic analyzer clips which uses a crappy pin that are formed by folding.
If you haven't gone so far down the development, I would have suggested reprogramming/re-purposing those $4-$6 "USBasp" cables from China to use as USB to SPI dongles. USBasp is open source programmer for AVR chips, so the Chinese copies would have same design. It uses V-USB, a bit-banging software USB stack. The 10 pin connector has power, AtMega8 SPI port and 1 GPIO line which is pretty much what you need to program SPI Flash. »www.fischl.de/usbasp/
There is a parallel port to SPI FLASH programmer that only require 4 resistors and a power source. I guess you have to magically obtain a copy of the firmware which tends to be the hard part.
rayer.g6.cz/programm/programe.htm look under SPIPGM.ZIP
>SPIPGM.ZIP ver. 2.1 [98 kB] (DOS/Win9x/NT/2k/XP/Vista/7/Linux) is a tool for programming serial SPI FlashROM memories attached to PC via parallel port cable. It can identify device, read, write, verify, erase and unlock flash memory. More info about needed hardware (CZ-only but schematics is self-explaining) here.