The recent rediscovery of magnetic field switchbacks or deflections embedded in the solar wind flow by the Parker Solar Probe mission lead to a huge interest in the modeling of the formation mechanisms and origin of these switchbacks. Several scenarios for their generation were put forth, ranging from lower solar atmospheric origins by reconnection, to being a manifestation of turbulence in the solar wind, and so on. Here we study some potential formation mechanisms of magnetic switchbacks in the lower solar atmosphere, using three-dimensional magnetohydrodynamic (MHD) numerical simulations. The model is that of an intense flux tube in an open magnetic field region, aiming to represent a magnetic bright point opening up to an open coronal magnetic field structure, e.g., a coronal hole. The model is driven with different plasma flows in the photosphere, such as a fast up-shooting jet, as well as shearing flows generated by vortex motions or torsional oscillations. In all scenarios considered, we witness the formation of magnetic switchbacks in regions corresponding to chromospheric heights. Therefore, photospheric plasma flows around the foot-points of intense flux tubes appear to be suitable drivers for the formation of magnetic switchbacks in the lower solar atmosphere. Nevertheless, these switchbacks do not appear to be able to enter the coronal heights of the simulation in the present model. In conclusion, based on the presented simulations, switchbacks measured in the solar wind are unlikely to originate from photospheric or chromospheric dynamics.