The hosts of long duration gamma-ray bursts (GRBs) are predominantly starburst galaxies at subsolar metallicity. At redshifts z < 1, this implies that most of them are low-mass galaxies similar to the populations of blue compact dwarfs and dwarf irregulars. What triggers the massive star-formation needed for producing a GRB progenitor is still largely unknown, as are the resolved gas properties and kinematics of these galaxies and their formation history. Here we present a sample of six spatially resolved GRB hosts at z < 0.3 observed with 3D spectroscopy at high spectral resolution (R = 8000−13 000) using FLAMES/VLT. We analyzed the resolved gas kinematics of the full sample and the abundances in a subsample with strong enough emission lines. Only two galaxies show a regular disk-like rotation field, another two are dispersion-dominated, and the remaining ones have two narrow emission components associated with different parts of the galaxy but no regular rotation field, which might indicate a recent merger. All galaxies show evidence for broad components underlying the main emission peak with σ of 50−110 km s−1. This broad component is more metal-rich than the narrow components, it is blueshifted in most cases, and it follows a different velocity structure. We find a weak correlation between the star-formation rate and the width of the broad component, its flux compared to the narrow component, and the maximum outflow velocity of the gas, but we do not find any correlation with the star-formation density, metallicity or stellar mass. We hence associate this broad component with a metal-rich outflow from star-forming regions in the host. The GRB is not located in the brightest region of the host, but is always associated with some star-forming region showing a clear wind component. Our study shows the great potential of 3D spectroscopy to study the star-formation processes and history in galaxies hosting extreme transients, the need for high signal-to-noise, and the perils using unresolved or only partially resolved data for these kinds of studies.