Cerebellar ataxia (CA) refers to the incoordination of movements of the eyes, speech, trunk, and limbs caused by cerebellar dysfunction. Conventional machine learning (ML) utilizes centralised databases to train a model of diagnosing CA. Despite the high accuracy, these approaches raise privacy concern as participants' data revealed in the data centre. Federated learning is an effective distributed solution to exchange only the ML model weight rather than the raw data. However, FL is also vulnerable to network attacks from malicious devices. In this study, we depict the concept of blockchained FL with individual's validators. We simulate the proposed approach with real-world dataset collected from kinematic sensors of CA individuals with four geographically separated clinics. Experimental results show the blockchained FL maintains competitive accuracy of 89.30%, while preserving both privacy and security.