Mapping three-dimensional (3-D) dynamic environments is essential for aerial robots but challenging to consider the increased dimensions in both space and time compared to 2-D static mapping. This paper presents a kernel-based 3-D dynamic occupancy mapping algorithm, K3DOM, that distinguishes between static and dynamic objects while estimating the velocities of dynamic cells via particle tracking. The proposed algorithm brings the benefits of kernel inference such as its simple computation, consideration of spatial correlation, and natural measure of uncertainty to the domain of dynamic mapping. We formulate the dynamic occupancy mapping problem in a Bayesian framework and represent the map through Dirichlet distribution to update posteriors in a recursive way with intuitive heuristics. The proposed algorithm demonstrates its promising performance compared to baseline in diverse scenarios simulated in ROS environments.