Plausible deniability (PD) allows at-risk users to deny the existence of their sensitive data stored on storage devices. This is critical to protect the privacy and the personal safety of users, as adversaries might force users to decrypt their devices, risking the disclosure of sensitive data that could endanger their lives and liberty. In this work, we show how current PD systems built on flash memory fail to obscure distinguishable data layouts created when hidden data is written. This deficiency makes them vulnerable to coercive adversaries who can capture single or multiple data snapshots of storage devices for scrutiny. To defend against this threat, we propose MUTE, a perMUTation-based PD systEm designed for flash memory. Building upon widely-adopted full disk encryption (FDE) mechanisms that provide device-level data encryption, MUTE modifies the distribution of initialization vectors (IVs) for encryption blocks within FDE, translating the hidden data into a permutation derived from the IV. Unlike other PD solutions, MUTE allows for storing hidden data without requiring the reduction of storage capacity. Moreover, it preserves the plausible deniability of the hidden data in a provably secure manner by maintaining the original logic of data operations on the flash memory without changing the data layout. We implement MUTE in the flash translation layer (FTL) of flash-based SSDs using FEMU, a widely-used emulator supporting flash memory research. Our evaluation with various micro-benchmarks and real-world workloads demonstrates that MUTE provides practical write and read throughputs of 23.4 MB/s and 15.7 MB/s and a capacity of 25.3 GB for hidden data in a 512 GB SSD, comparable with existing PD systems. MUTE achieves strong PD guarantees for flash-based devices against coercive adversaries, outperforming current PD systems.