We present a full three-dimensional (3D) power flow analysis of an emitter-nanoantenna system. A conventional analysis, based on the total Poynting vector, calculates only the coupling strength in terms of the Purcell enhancement. For a better understanding of the emitter-nanoantenna system, not only the Purcell enhancement but also complete information on the energy transfer channels is necessary. The separation of the pure scattering and emitter output Poynting vectors enables the quantification of the individual energy transfer channels. Employing the finite-difference time-domain method (FDTD), we examine a nanodisk antenna that supports the bright dipole and dark quadrupole resonance modes for which the power flow characteristics are completely distinct, and we analyze the power flow enhancements to the energy transfer channels with respect to the wavelength, polarization, and position of the emitter coupled to the antenna. The 3D power flow analysis reveals how the constructive or destructive interference between the emitter and the antenna resonance mode affects the power flow enhancements and the far-field radiation pattern. Our proposed power flow analysis should play a critical role in characterizing the emitter-antenna system and customizing its energy transfer properties for desired applications.