A model of spin relaxation of Kondo lattices is proposed to explain the angular dependence of the electron spin resonance (ESR) parameters in the heavy fermion compounds Y bIr(2)Si(2) and Y bRh(2)Si(2). A perturbational scaling approach reveals a collective spin motion of Yb ions with conduction electrons in the bottleneck regime. A common energy scale due to the Kondo effect regulates the temperature dependence of different kinetic coefficients to result in a mutual cancelation of all divergent parts in a collective spin mode. The angular dependence of the ESR intensity, linewidth and resonant frequency is shown to be in good agreement with experimental data on Y bIr(2)Si(2) and Y bRh(2)Si(2). In particular, the unexpectedly weak dependence of the ESR intensity on the orientation of the microwave magnetic field agrees with the properties of the discussed model.