Understanding the variability of low-level atmospheric circulation regimes is key for understanding the dynamics of monsoon systems. The South American Monsoon is characterized by strong year-long trade winds that are channeled southward into the South American Low-Level Jet after crossing the Amazon basin, which in turn is elementary for the moisture transport to Southern South America. In this study, we utilize streamflow wind networks, a type of climate networks that tracks the local flow of the wind field, together with the analysis of composites of wind, precipitation, and geopotential height fields, to investigate the variability of the South American low-level circulation. The streamflow wind networks are used here as they are able to directly track the wind flow and encode its spatiotemporal characteristics in their topology. We focus on intraseasonal variations in terms of active and break monsoon phases on the one hand, and on the interannual variability in terms of the impacts of the El Niño-Southern Oscillation on the other hand. Our findings highlight the importance of the South American Low-Level Jet, its spatial position and variability. Our study reveals the relation of the active and break regimes to anomalous high- and low-pressure systems over the southern Atlantic that are connected to Rossby wave trains from the southern Pacific, as well as the impact of these regimes on the cross-equatorial low-level flow. In addition, the streamflow networks that we use demonstrate significant shifts of the dominant wind flow pattern during El Niño and La Niña episodes.