Flashrom [1] is the go-to tool for everything SPI on *nix. It knows how to identify chips and will prevent you from doing anything stupid, if it can.
[1]: https://www.flashrom.org/Flashrom
(As of January, it looks to have support for your $3 programmer! https://github.com/flashrom/flashrom/blob/86bb6c55dd3bb1a167... )