Abstract: Propagating kink waves have been reported recently and have been found to be ubiquitous in the solar corona including in the quiet Sun. It is imperative to understand the mechanisms that enable their energy to be transferred to the plasma. Carrying on the legacy of the standing kink waves, mode conversion via resonant absorption is thought to be one of the main mechanisms for damping of these propagating kink waves, and is considered to play a key role in the process of energy transfer. We use the Doppler velocity images of the Coronal Multi-channel Polarimeter (CoMP) for the study of propagating kink waves in quiescent coronal loops. A coherence-based method is used to track the Doppler velocity signal of the waves, enabling an investigation into the spatial evolution of velocity perturbations. To enable accurate estimates of these quantities, the first derivation is provided of a likelihood function suitable for fitting models to the ratio of two power spectra obtained from discrete Fourier transforms. Maximum likelihood estimation is used to fit an exponential damping model to the observed variation in power ratio as a function of frequency. This also confirms earlier indications that propagating kink waves are undergoing frequency-dependent damping. Additionally, it is found that the rate of damping decreases for longer coronal loops that reach higher in the corona. The analysis techniques are used to create a statistical sample of quiescent loops to study the statistical properties of propagating kink waves and compare it to the studies of standing kink waves. It is noted that the damping for the propagating waves appears to be significantly weaker than that found from measurements of standing kink modes. The propagating kink waves also exhibit signatures of power amplification of waves. These propagating kink waves provide a new avenue to perform coronal magneto-seismology even during the quiet Sun period and this reliable method is not limited by requiring the eruptive activity of the Sun.