2D finite dust clusters are systems of small number of charged grains immersed in the plasma. The particle-in-cell (PIC) simulations are used to study the plasma structure, potential field and distributions of ion, electron and charge density within a dust cluster consisting of 19 grains in the absence and presence of a directed ion flow. In the isotropic plasma, an energetically stable configuration of this 2D finite dust cluster is found with overlapping ion clouds within the cluster's area. The supersonic ion flow transforms the common potential well to a shallow oval basin with the formation of an elongated potential hill behind the dust cluster. The common wake region with strong ion focusing is developed with the number density of ions significantly exceeding that in bulk plasma and within a cluster. The region within a dust cluster remains highly depleted of electrons even at supersonic ion flows. The charge on one of grains switches to a positive value. The kinetic-level PIC results provide insights into development of instabilities that can initiate the cluster reorganization, disordering and melting.