We study the imprints of boxy/peanut structures on the 2D line-of-sight kinematics of simulated disc galaxies. The models under study belong to a family with varying initial gas fraction and halo triaxiality, plus few other control runs with different structural parameters; the kinematic information was extracted using the Voronoi-binning technique and parametrized up to the fourth order of a Gauss–Hermite series. Building on a previous work for the long-slit case, we investigate the 2D kinematic behaviour in the edge-on projection as a function of the boxy/peanut strength and position angle; we find that for the strongest structures the highest moments show characteristic features away from the mid-plane in a range of position angles. We also discuss the masking effect of a classical bulge and the ambiguity in discriminating kinematically this spherically symmetric component from a boxy/peanut bulge seen end-on. Regarding the face-on case, we extend existing results to encompass the effect of a second buckling and find that this phenomenon spurs an additional set of even deeper minima in the fourth moment. Finally, we show how the results evolve when inclining the disc away from perfectly edge-on and face-on. The behaviour of stars born during the course of the simulations is discussed and confronted to that of the pre-existing disc. The general aim of our study is providing a handle to identify boxy/peanut structures and their properties in latest generation Integral Field Unit observations of nearby disc galaxies.