Context. The physics of magnetic hot stars and how a large-scale magnetic field affects their interior properties is largely unknown. Few studies have combined high-quality observations and modelling of magnetic pulsating stars, known as magneto-asteroseismology, primarily because of the dearth of detected pulsations in stars with a confirmed and well-characterised large-scale magnetic field. Aims. We aim to characterise observational signatures of rotation and pulsation in chemically peculiar candidate magnetic stars using photometry from the K2 space mission. Thus, we identify the best candidate targets for ground-based, optical spectropolarimetric follow-up observations to confirm the presence of a large-scale magnetic field. Methods. We employed customised reduction and detrending tools to process the K2 photometry into optimised light curves for a variability analysis. We searched for the periodic photometric signatures of rotational modulation caused by surface abundance inhomogeneities in 56 chemically peculiar A and B stars. Furthermore, we searched for intrinsic variability caused by pulsations (coherent or otherwise) in the amplitude spectra of these stars. Results. The rotation periods of 38 chemically peculiar stars are determined, 16 of which are the first determination of the rotation period in the literature. We confirm the discovery of high-overtone roAp pulsation modes in HD 177765 and find an additional 3 Ap and Bp stars that show evidence of high-overtone pressure modes found in roAp stars in the form of possible Nyquist alias frequencies in their amplitude spectra. Furthermore, we find 6 chemically peculiar stars that show evidence of intrinsic variability caused by gravity or pressure pulsation modes. Conclusions. The discovery of pulsations in a non-negligible fraction of chemically peculiar stars make these stars high-priority targets for spectropolarimetric campaigns to confirm the presence of their expected large-scale magnetic field. The ultimate goal is to perform magneto-asteroseismology and probe the interior physics of magnetic pulsating stars.