The physical mechanisms that produce the slow solar wind are still highly debated. Parker Solar Probes (PSPs) second solar encounter provided a new opportunity to relate in situ measurements of the nascent slow solar wind with white-light images of streamer flows. We exploit data taken by the Solar and Heliospheric Observatory (SOHO), the Solar TErrestrial RElations Observatory (STEREO) and the Wide Imager on Solar Probe to reveal for the first time a close link between imaged streamer flows and the high-density plasma measured by the Solar Wind Electrons Alphas and Protons (SWEAP) experiment. We identify different types of slow winds measured by PSP that we relate to the spacecrafts magnetic connectivity (or not) to streamer flows. SWEAP measured high-density and highly variable plasma when PSP was well connected to streamers but more tenuous wind with much weaker density variations when it exited streamer flows. STEREO imaging of the release and propagation of small transients from the Sun to PSP reveals that the spacecraft was continually impacted by the southern edge of streamer transients. The impact of specific density structures is marked by a higher occurrence of magnetic field reversals measured by the FIELDS magnetometers. Magnetic reversals originating from the streamers are associated with larger density variations compared with reversals originating outside streamers. We tentatively interpret these findings in terms of magnetic reconnection between open magnetic fields and coronal loops with different properties, providing support for the formation of a subset of the slow wind by magnetic reconnection.