Molten carbonate fuel cell configurations are provided that allow for introduction of an anode input gas flow on a side of the fuel cell that is adjacent to the entry side for the cathode input gas flow while allowing the anode and cathode to operate under co-current flow and/or counter-current flow conditions. It has been discovered that improved flow properties can be achieved within the anode or cathode during co-current flow or counter-current flow operation by diverting the input flow for the anode or cathode into an extended edge seal region (in an extended edge seal chamber) adjacent to the active area of the anode or cathode, and then using a baffle to provide sufficient pressure drop for even flow distribution of the anode input flow across the anode or cathode input flow across the cathode. A second baffle can be used to create a pressure drop as the anode output flow or cathode output flow exits from the active area into a second extended edge seal region (in a second extended edge seal chamber) prior to leaving the fuel cell.