TL;DRI was going to write a giant wall of math, but I'll stick to this for now:Wrong!
1. Rewrite formula
If 1/x' = 1/c + k/x then
1/x' = x/cx + ck/cx
1/x' = (x + ck) / cx
x' = cx / (x + ck)
Note that you can also write this as c*r / (r + ckq) with r = rating and q = rating conversion rate
This formula then also becomes correct for Armor, with a c = 1 and kq = K as most people know it.
2. Damage comparison
The damage that goes through is past avoidance is
1-x' = (x + ck -cx) / (x + ck)
Any change in pre-DR avoidance can be written as
1-y' = (x + d + ck - cx - cd) / (x + d + ck)
with y' = new avoidance and d = change in pre-DR avoidance
The relative damage change is then new damage / old damage or
(1-y') / (1-x')
3. The Math
(1-y') / (1-x') = [(x + d + ck - cx - cd) / (x + d + ck)] / [cx / (x + ck)]
(1-y') / (1-x') = [(x + d + ck - cx - cd) * ( x + ck) ] / [(x + d + ck) * cx]
(1-y') / (1-x') = [(x² + dx + ckx - cx² - cdx) + (ckx + cdk + c²k² - c²kx - c²dk) ] / (cx² + cdx + c²kx)
(1-y') / (1-x') = [(1-c²)x² + (d+2ck-cd-c²k)x+ck*(d+ck-cd)] / (cx² + cdx + c²kx)
And no matter how you rewrite that, you can never remove x as a variable, thus there is no fixed value of damage reduction per d.
This could also be seen from step 1, where the formula is extremely similar to the armor formula, of which we know it is not lineair with relative damage reduction.
In fact, the only stat I ever know to scale as you say is Resilience, because it worked as x' = 1 - a^(k*x)
But the problem with this formula is that it is relatively demanding of server calculations, due to the power part.
4. Extra info
* This is all without actually considering base avoidance, which is not part of the DR formula, but counts towards your efficiency. And as different races have different base dodge/parry, it would simply never be equal for all classes, no matter how you write this out.
* x' = x when c / (x + ck) = 1, or c = x + ck. Write as x = c - ck = (1-k)c. For Parry this is 10.436% from Strength/rating a,d for dodge this is 3.99% or resp. 9236 parry rating (str conversion included) and 3530 dodge rating . Anything below that and you will actually gain more dodge/parry chance than you have pre-DR!