Recently, Mixture-of-Experts (MoE) models have gained attention for efficiently scaling large language models. Although these models are extremely large, their sparse activation enables inference to be performed by accessing only a fraction of the model at a time. This property opens the possibility of on-device inference of MoE, which was previously considered infeasible for such large models. Consequently, various systems have been proposed to leverage this sparsity and enable efficient MoE inference for edge devices. However, previous MoE inference systems like Fiddler[8] or DAOP[13] rely on DRAM-based offloading and are not suitable for memory constrained on-device environments. As recent MoE models grow to hundreds of gigabytes, RAM-offloading solutions become impractical. To address this, we propose FlashMoE, a system that offloads inactive experts to SSD, enabling efficient MoE inference under limited RAM. FlashMoE incorporates a lightweight ML-based caching strategy that adaptively combines recency and frequency signals to maximize expert reuse, significantly reducing storage I/O. In addition, we built a user-grade desktop platform to demonstrate the practicality of FlashMoE. On this real hardware setup, FlashMoE improves cache hit rate by up to 51% over well-known offloading policies such as LRU and LFU, and achieves up to 2.6x speedup compared to existing MoE inference systems.