  The paper is devoted to generic translation flows corresponding to Abelian
differentials on flat surfaces of arbitrary genus $g\ge 2$. These flows are
weakly mixing by the Avila-Forni theorem. In genus 2, the H\"older property for
the spectral measures of these flows was established in our papers [10,12].
Recently Forni [17], motivated by [10], obtained H\"older estimates for
spectral measures in the case of surfaces of arbitrary genus. Here we combine
Forni's idea with the symbolic approach of [10] and prove H\"older regularity
for spectral measures of flows on random Markov compacta, in particular, for
translation flows in all genera.
