Reconfigurable Intelligent Surface (RIS) panels are envisioned as a key technology for sixth-generation (6G) wireless networks, providing a cost-effective means to enhance coverage and spectral efficiency. A critical challenge is the estimation of the cascaded base station (BS)-RIS-user channel, since the passive nature of RIS elements prevents direct channel acquisition, incurring prohibitive pilot overhead, computational complexity, and energy consumption. To address this, we propose a deep learning (DL)-based channel estimation framework that reduces pilot overhead by grouping RIS elements and reconstructing the cascaded channel from partial pilot observations. Furthermore, conventional DL models trained under single-user settings suffer from poor generalization across new user locations and propagation scenarios. We develop a distributed machine learning (DML) strategy in which the BS and users collaboratively train a shared neural network using diverse channel datasets collected across the network, thereby achieving robust generalization. Building on this foundation, we design a hierarchical DML neural architecture that first classifies propagation conditions and then employs scenario-specific feature extraction to further improve estimation accuracy. Simulation results confirm that the proposed framework substantially reduces pilot overhead and complexity while outperforming conventional methods and single-user models in channel estimation accuracy. These results demonstrate the practicality and effectiveness of the proposed approach for 6G RIS-assisted systems.