The stiffness of a flange is related to the stiffness of the bolted joint. this means that Km is related to Kb. the formula can be located in any engineer's design handbook. the most common one is by Shigely. Just in case you cannot find it the formular for Km is given as

Km=dAE e(b(d/lm)

mmud9613:  Flange stiffness k_m, assuming compression zone frusta in bolt grip region, is computed as follows per Shigley, Mechanical Engineering Design, McGraw-Hill, 1989, p. 340, Eq. 8-13, where k_i is stiffness of ith plate (layer) truncated frustum.

k_m = 1/summation(1/k_i).

k_i = pi E_i dh_i tan(alpha)
   /ln[ (2 t_i tan(alpha)   +   d_i  -  dh_i)(d_i + dh_i)
      /((2 t_i tan(alpha)   +   d_i  +  dh_i)(d_i - dh_i)) ].

where
alpha = compression frustum apex half angle.
E_i = ith layer modulus of elasticity.
t_i = ith layer thickness.
d_i = outer diameter of outer end of ith truncated frustum layer.
dh_i = ith layer hole diameter.
pi = 3.141593.

shigley provides a pretty good formular but if you use this then you will have to use all of shigleys formulars otherwise solutions will vary. his way of doing things are right only if you use it from the begining.

Have you looked in "Roark's Formulas for Stress & Strain",published by McGraw-Hill?