We map the 3D kinematics of the Galactic disc out to 3.5 kpc from the Sun, and within 0.75 kpc from the midplane of the Milky Way. To this end, we combine high quality astrometry from Gaia EDR3, with the radial velocities from Gaia DR2, and from major spectroscopic surveys including APOGEE, GALAH, and LAMOST. We construct an axisymmetric model for the mean velocity field, and then subtract this on a star-by-star basis to obtain the peculiar velocity field in the Galactocentric components, 𝑉 𝜙 , 𝑉 𝑅 , 𝑉 𝑧 , as well as the heliocentric lineof-sight, 𝑉 los . The velocity residuals are quantified using the power spectrum, and we find that the peak power (𝐴) in the midplane (|𝑧| < 0.25 kpc) is (𝐴 𝜙 , 𝐴 R , 𝐴 Z , 𝐴 los )=(4.2, 8.5, 2.6, 4.6), at 0.25 < |𝑧|/[kpc] < 0.5, is (𝐴 𝜙 , 𝐴 R , 𝐴 Z , 𝐴 los )=(4.0, 7.9, 3.6, 5.3), and at 0.5 < |𝑧|/[kpc] < 0.75, is (𝐴 𝜙 , 𝐴 R , 𝐴 Z , 𝐴 los )=(1.9, 6.9, 5.2, 6.4). Our results provide for the first time, a measure of the streaming motion in the disc in the individual components. We find that streaming is most significant in the Galactocentric radial component, and at all heights (|𝑍 |) probed, but is also not negligible in the other components. Additionally, we find that the patterns in the velocity field overlap spatially with models for the Spiral arms in the Milky Way. Finally, we demonstrate using a simulation that phase mixing of disrupting spiral arms can generate such residuals in the velocity field, where the radial component is dominant, just as in the real data. The simulation also suggests that with evolution of time both the amplitude and the physical scale of the peculiar motion decreases.