We continue our study of chaotic mixing and transport of passive particles in a simple model of a meandering jet flow [Prants et al., Chaos 16, 033117 (2006)]. In the present paper we study and phenomenologically explain a connection between dynamical, topological, and statistical properties of chaotic mixing and transport in the model flow in terms of dynamical traps, singular zones in the phase space where particles may spend an arbitrarily long but finite time [Zaslavsky, Phys. D 168-169, 292 (2002)]. The transport of passive particles is described in terms of lengths and durations of zonal flights which are events between two successive changes of sign of zonal velocity. Some peculiarities of the respective probability density functions for short flights are proven to be caused by the so-called rotational-island traps connected with the boundaries of resonant islands (including the vortex cores) filled with the particles moving in the same frame and the saddle traps connected with periodic saddle trajectories. Whereas, the statistics of long flights can be explained by the influence of the so-called ballistic-islands traps filled with the particles moving from a frame to frame.