How does one calculate the uncertainties of an out of calibration VNA and calibration kit bought on ebay?
In an ideal world everyone would do as you ask. But the nanoVNA has made it possible for people with relatively little or no VNA experience to have one. And many only have experience with hobby grade VNAs.
Even well educated people with extensive experience with professional grade VNAs often lack the mathematical skills to do completely rigorous analyses of their measurements.
I'd like to urge you to write a document describing how to do what you ask within the constraints of what is available to the individuals making the measurements. My undergraduate degree was English lit, but I'm a PhD level geophysicist with very strong mathematical skills. I don't know how to do what you ask, though I'm sure I will eventually learn. If you will create a rough draft and post it in the Files section, I'll help with polishing up your English.