Maths with a Keyboard. Here we gooo:
The chance to flinch given by a King's Rock on a move with already a flinch chance is calculated with this formula: "flinch rate" + ("flinch rate"- 1)x .1
So that means flinch rate = 30 + (30 - 1)x .1
= 30 + 29 x .1
= 30 + 2.9
So henceforth the flich chance for a Rock Slide benefitting from King's Rock will be 32.1%
Source: This for the formula and the rest is basic arithmetics.
EDIT: This is for until Gen 5, and since then, flinch rates do not stack anymore. Sorry I realized this after all that stupidity lol.
Hope I helped!