C0G does not exhibit piezoelectricity.
They probably exhibit a small amount of electrostriction, which informally might look the same (an electromechanical coupling), but is a different phenomenon.
Most materials exhibit this property, as well as the analogous effect, magnetostriction.
If nothing else, you can think of the electric attraction between the plates acting to compress the dielectric, which has finite rigidity (elastic modulus), and therefore increasing the capacitance slightly at the same time. (That change may manifest as a dependent increase in value, or as a loss component. That change is likely swamped by much stronger effects, such as saturation in ferromagnetic cores.)
As for the magnitude, if you can figure out the composition of the capacitors, and find academic articles discussing the material properties, that's probably the best you'll find.
In complete capacitors, it seems like an ill-posed problem: there is no obvious preferred direction to apply force to a chip capacitor, that would be both general and useful. So I wouldn't think you'd find an article discussing that particular application, or if you do, it may not be very useful.
(Yes, applying pressure in the "stack of plates" direction would be the most obvious -- but a board-flex strain is most likely to be applied in a real circuit, which is very different. Conversely, it's not obvious how one could quantify board-flex strains: it depends on solder amount, pad size, chip height, board material and temperature, and so on.)
For the same reason, it might be more beneficial to measure things yourself. Don't forget to measure with an applied bias (polarization): if the material is electrostrictive, you will observe an output proportional to bias. Ideally you'd have an accelerometer on the board as well, but if you simply whack the board in a consistent manner (hammer it with a solenoid, in a repeatable setup?), that would be okay for qualitative comparisons between component types.
Tim