Stacked intelligent metasurfaces (SIMs) have recently gained attention as a paradigm for wave-domain signal processing with reduced reliance on costly radio-frequency (RF) chains. However, conventional SIMs rely on uniform inter-layer spacing and require deep stacking to ensure processing capability, resulting in severe power attenuation in practice. To address this issue, we propose a flexible intelligent layered metasurface (FILM) architecture consisting of two shape-controllable flexible metasurface layers. By replacing rigid metasurfaces with flexible ones in both layers, the transmission coefficient matrix can be dynamically adjusted, significantly decreasing the number of required layers while maintaining signal processing performance. Firstly, we develop a two-layer FILM-assisted multi-user multiple-input single-output (MU-MISO) system, wherein we formulate a channel fitting problem aimed at reducing the difference between the FILM-induced and target channels. Then, we solve this non-convex problem by employing an alternating optimization (AO) method, featuring closed-form phase shift updates and a gradient descent-based shape optimization. Furthermore, we analyze the upper bound on sum-rate and the complexity of computation to provide insights into design trade-offs. Finally, simulation results demonstrated that the proposed transmissive FILM architecture achieves over 200\% improvement in sum-rate and more than 7 dB bit-error rate (BER) gain compared to the conventional seven-layer SIMs.