How to make -12V from a +12V supply?
If your three power supplies are isolated from their input, which is most likely the case if they are line powered, then what you propose should work fine.

A isolated power supply produces a voltage difference not some absolute voltage.  This voltage difference is usually talked about with the assumption that the negative side will be considered the 0 V reference.  This simplifies descriptions and calculations, and is often exactly what will be done with the supply.  However, there is no rule that says the negative output must be connected to what the rest of the system considers 0 V.

Note that this can only go so far.  There should be a spec as to what the maximum isolation voltage for the supply is.  This says how far the output can float relative to the input.  That might be 1000 V, for example, for a line-powered supply.  If you put more than that between output and input, the result could be pyrotechnics.

Again, the above is all assuming this is a isolated supply.  Most line-powered supplies are isolated.  If it only has a two-prong plug, then it should be isolated.  Some bench supplies have three output terminals, the floating differential output and the line ground brought out to a terminal.  These usually have a optional grounding strap you can connect between the ground terminal or either output, or leave disconnected to let the output float.