Does Kirchhoff's law apply to displacement currents?
Displacement currents inside most circuits are limited to the space between capacitor plates (AFAIK). Outside circuits, the EM waves have changing electric field, so they too involve displacement current.
Kirchhoff's laws are based on the approximations / simplification made based on conservation of Energy (KVL) and conservation of charge (KCL) when applied to lumped element approximations of circuits.
[Wikipedia]

Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits.

In lumped parameter models, the capacitor is a lumped device, i.e., a point and so the gap between the plates are not modelled. They also do not deal with EM radiations (AFAIK). So both opportunities to use the concept of displacement current do not exist in those circuits which are modelled by lumped element models.