Context. Obtaining reliable distance estimates to gas clouds within the Milky Way is challenging in the absence of certain tracers. The kinematic distance approach has been used as an alternative, and it is derived from the assumption of circular trajectories around the Galactic centre. Consequently, significant errors are expected in regions where gas flow deviates from purely circular motions. Aims. We aim to quantify the systematic errors that arise from the kinematic distance method in the presence of a Galactic potential that is non-axisymmetric. We investigated how these errors differ in certain regions of the Galaxy and how they relate to the underlying dynamics. Methods. We performed 2D isothermal hydrodynamical simulation of the gas disk with the moving-mesh code AREPO, adding the capability of using an external potential provided by the AGAMA library for galactic dynamics. We introduced a new analytic potential of the Milky Way, taking elements from existing models and adjusting parameters to match recent observational constraints. Results. In line with results of previous studies, we report significant errors in the kinematic distance estimate for gas close to the Sun along sight lines towards the Galactic centre and anti-centre and associated with the Galactic bar. Kinematic distance errors are low within the spiral arms, as gas resides close to local potential minima and the resulting line-of-sight velocity is similar to what is expected for an axisymmetric potential. Interarm regions exhibit large deviations at any given Galactic radius, and this is caused by the gas being sped up or slowed down as it travels into or out of spiral arms. In addition, we identify 'zones of avoidance' in the lv-diagram, where the kinematic distance method is particularly unreliable and should only be used with caution, and we find a power-law relation between the kinematic distance error and the deviation of the projected line-of-sight velocity from circular motion.