Flash ADC's nonlinear output and response
Flash ADCs normally use a set of comparators, one per LSB, that use equally-spaced reference voltages developed from a string of equal-value resistors. What the author is saying is that the spacing of the reference voltages can be modified to implement a non-linear input-to-digital mapping.
A good example of a possible use of non-linear spacing is for a camera ADC, that implements gamma correction (tone mapping) at the ADC itself. There are many papers about this idea. It seemed popular about 5 years ago, but never really caught on. Probably because making unequally-spaced resistances with precision and repeatability in silicon posed some difficulty.
At any rate, instead of analog non-linear sampling, what's done for sensors now is to use higher resolution linear ADCs, and re-map their levels in the digital domain using a technique called piecewise linear mapping, or PWL. The overall result is the same however: tones are mapped more usefully to match human visual response, that makes maximum use of the numerical range available.