Autonomous ocean-exploring vehicles have begun to take advantage of onboard sensor measurements of water properties such as salinity and temperature to locate oceanic features in real time. Such targeted sampling strategies enable more rapid study of ocean environments by actively steering towards areas of high scientific value. Inspired by the ability of aquatic animals to navigate via flow sensing, this work investigates hydrodynamic cues for accomplishing targeted sampling using a palm-sized robotic swimmer. As proof-of-concept analogy for tracking hydrothermal vent plumes in the ocean, the robot is tasked with locating the center of turbulent jet flows in a 13,000-liter water tank using data from onboard pressure sensors. To learn a navigation strategy, we first implemented Reinforcement Learning (RL) on a simulated version of the robot navigating in proximity to turbulent jets. After training, the RL algorithm discovered an effective strategy for locating the jets by following transverse velocity gradients sensed by pressure sensors located on opposite sides of the robot. When implemented on the physical robot, this gradient following strategy enabled the robot to successfully locate the turbulent plumes at more than twice the rate of random searching. Additionally, we found that navigation performance improved as the distance between the pressure sensors increased, which can inform the design of distributed flow sensors in ocean robots. Our results demonstrate the effectiveness and limits of flow-based navigation for autonomously locating hydrodynamic features of interest.