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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 Galaxy. To this end, we combine high quality astrometry from \gedrthree{}, with heliocentric line-of-sight velocities from \gdrtwo{}, and spectroscopic surveys including \apogee{}, \galah{}, and \lamost{}. We construct an axisymmetric model for the mean velocity field, and subtract this on a star-by-star basis to obtain the residual velocity field in the Galactocentric components (\vphi{}, \vR, \vz), and \vlos{}. The velocity residuals are quantified using the power spectrum, and we find that the peak power ($A/$[\rm \kms{}]) in the midplane ($|z|<0.25$ kpc) is ($A_ϕ,A_{\rm R},A_{\rm Z},A_{\rm los}$)=($4.2,8.5,2.6,4.6$), at $0.25 < |z|/[{\rm kpc}] < 0.5$, is ($A_ϕ,A_{\rm R},A_{\rm Z},A_{\rm los}$)=($4.0,7.9,3.6,5.3$), and at $0.5 < |z|/[{\rm kpc}] < 0.75$, is ($A_ϕ,A_{\rm R},A_{\rm Z},A_{\rm los}$)=($1.9,6.9,5.2,6.4$). Our results provide a sophisticated measurement of the streaming motion in the disc and in the individual components. We find that streaming is most significant in \vR, and at all heights ($|Z|$) probed, but is also non-negligible in other components. Additionally, we find that patterns in velocity field overlap spatially with models for Spiral arms in the Galaxy. Our simulations show that phase-mixing of disrupting spiral arms can generate such residuals in the velocity field, where the radial component is dominant, just as in real data. We also find that with time evolution both the amplitude and physical scale of the residual motion decrease.