Usually, it is difficult to observe Compton scattering in an atom. One way to overcome this difficulty is to allow a multiphoton to collide with an atom. This phenomenon is called multiphoton Compton scattering (MCS) phenomenon. Thus, we can investigate the MCS in the visible light region. The cluster atoms move as a whole, namely atomic Dicke states, and the multiphoton interacts with cluster atoms. We can observe a significant Doppler shift of resonant fluorescence spectrum (RFS) in a room-temperature two-level ${}^{85}$Rb atomic system. In this paper, we present a detailed analysis of the physics mechanism of the Doppler shift and propose a method to measure the component of the Dicke states (the atomic polymers with different masses) by using the Doppler shift of the RFS.