Efficient point-to-point navigation in the presence of a background flow field is important for robotic applications such as ocean surveying. In such applications, robots may only have knowledge of their immediate surroundings or be faced with time-varying currents, which limits the use of optimal control techniques for planning trajectories. Here, we apply a novel Reinforcement Learning algorithm to discover time-efficient navigation policies to steer a fixed-speed swimmer through an unsteady two-dimensional flow field. The algorithm entails inputting environmental cues into a deep neural network that determines the swimmer's actions, and deploying Remember and Forget Experience replay. We find that the resulting swimmers successfully exploit the background flow to reach the target, but that this success depends on the type of sensed environmental cue. Surprisingly, a velocity sensing approach outperformed a bio-mimetic vorticity sensing approach by nearly two-fold in success rate. Equipped with local velocity measurements, the reinforcement learning algorithm achieved near 100% success in reaching the target locations while approaching the time-efficiency of paths found by a global optimal control planner.