A k-dominating set in a graph G = (V,E) is a set U ⊆ V such that ever vertex of G is either in U or has at least k neighbors in U . In this paper we give simple distributed approximation algorithms in the local model for the minimum k-dominating set problem for k ≥ 2 in graphs with no K3,h-minor and graphs with no K4,4-minor. In particular, this gives fast distributed approximations for graphs of bounded genus and linklessly embeddable graphs. The algorithms give a constant approximation ratio and run in a constant number of rounds. In addition, we will give a (1 + )-approximation for an arbitrary fixed > 0 which runs in O(log∗ n) rounds where n is the order of a graph.