You can use a chip clip, but presumably you rejected that idea because your objective is for this to be replicable by the kind of people who don't know what a chip clip is.
I knew I wanted one, but I didn't know that it was called a "chip clip" and indeed "IC clip" and "IC test clip" seem to be a better match.
The clip will give you a electrical connection to the SPI flash but I'm not sure you'll be able to talk to it without jumpers on the board. Is it possible without jumpers?