In recent years large attention in statistics has focused on dimensionally reduced model-based clustering methods, such as Mixtures of Factor Analyzers, which simultaneously cluster and reduce dimensions using latent variables. Unlike the classical formulation based on Gaussian factors, several adaptations have been made to model complex, non-Gaussian, and diverse data. This work employs quantile-based distributions to model latent variables within factor models, assuming conditional independence among factors. While offering a flexible and parsimonious parameterization, the use of quantile functions increases computational costs, particularly in Bayesian inference. We explore Bayesian estimation of flattened generalized logistic distributions, and then we generalize the model to a mixtures of factor models, providing insights into complex and heterogeneous data structures.