The chameleon screening mechanism has been constrained many a time using dynamic and kinematic galaxy cluster observables. Current constraints are, however, insensitive to different mass components within galaxy clusters and have been mainly focused on a single mass density profile, the Navarro-Frenk-White mass density model. In this work, we extend the study of the Chameleon screening mechanism in galaxy clusters by considering a series of mass density models, namely: generalized-Navarro-Frenk-While, b-Navarro-Frenk-While, Burket, Isothermal and Einasto. The coupling strength (β) and asymptotic value of the chameleon field (ϕ∞) are constrained by using kinematics analyses of simulated galaxy clusters, generated both assuming General Relativity and a strong chameleon scenario. By implementing a Bayesian analysis we comprehensively show that the biases introduced due to an incorrect assumption of the mass model are minimal. Similarly, we also demonstrate that a spurious detection of evidence for modifications to gravity is highly unlikely when utilizing the kinematics of galaxy clusters.