<p>Deploying neural networks across devices with vastly different computational budgets is critical for realizing AI Flow at the network edge. This paper contributes to cooperative family-model systems by proposing a single network that can be dynamically sliced into subnetworks of varying sizes, enabling seamless adaptation to heterogeneous resource constraints across the device-edge-cloud continuum. To scale broadly, we make both the width and depth of the network flexible. For width scaling, we introduce FlexAttention, which enables a variable number of attention heads to adaptively adjust computational load. We also propose FlexRMSNorm, a normalization layer that dynamically adapts to different network widths. Combined with early-exit strategies, these components form a network that scales in both width and depth. Built from these flexible modules, we present SEFlow, a causal and sampling-rate-agnostic model that handles a wide range of speech enhancement tasks, including denoising, dereverberation, declipping, and packet loss concealment. Experimental results demonstrate that SEFlow is comparable to the state-of-the-art task-specific models across multiple speech enhancement tasks. Remarkably, even sub-networks as small as 1% of the full network remain effective in low-resource scenarios. Our demonstrations are available on the <a href="https://linfeng-feng.github.io/SEFlow-demo/">project homepage.</a></p>