Medical imaging is key in modern medicine. From magnetic resonance imaging (MRI) to microscopic imaging for blood cell detection, diagnostic medical imaging reveals vital insights into patient health. To predict diseases or provide individualized therapies, machine learning techniques like kernel methods have been widely used. Nevertheless, there are multiple challenges for implementing kernel methods. Medical image data often originates from various hospitals and cannot be combined due to privacy concerns, and the high dimensionality of image data presents another significant obstacle. While randomised encoding offers a promising direction, existing methods often struggle with a trade-off between accuracy and efficiency. Addressing the need for efficient privacy-preserving methods on distributed image data, we introduce OKRA (Orthonormal K-fRAmes), a novel randomized encoding-based approach for kernel-based machine learning. This technique, tailored for widely used kernel functions, significantly enhances scalability and speed compared to current state-of-the-art solutions. Through experiments conducted on various clinical image datasets, we evaluated model quality, computational performance, and resource overhead. Additionally, our method outperforms comparable approaches