Measurements of three-dimensional correlation functions of like-sign low transverse momentum kaon pairs from Au+Au collisions at top RHIC energy $sqrt s_{NN}$=200 GeV are presented. The extracted kaon source function is narrower than the pion one and does not have the long tail along the pair transverse momentum direction. This indicates a much smaller role of long-lived resonance decays and/or of the emission duration on kaon emission. Three-dimensional Gaussian shape of the kaon source function can be adequately reproduced by Therminator simulations with resonance contributions taken into account. Comparison to pion data at the same energy reveals that the kaon Gaussian radii in the outward and sideward directions scale with the transverse mass $m_T$. In the longitudinal direction, unlike at lower SPS energies, the Gaussian radii do not seem to follow the exact $m_T$ scaling between kaons and pions.