Simulating the dynamics of large-scale many-fermion systems is a longstanding goal of quantum chemistry, materials science and condensed matter. Local fermion-to-qubit encodings have opened a new path for practical fermionic simulations on digital qubit-based quantum hardware. In this work, we explore these local encodings from the perspective of the corresponding time-evolution unitaries. Specifically, we propose a new framework for digital implementations of qubit-encoded fermionic time-evolution unitaries based on flow sets, which are one-dimensional subsets of the directed fermionic interaction graph. We find that any local fermionic encoding, when restricted to a given flow set, adopts a simple structure that we classify systematically. For each categorized flow set form, we propose a low-depth qubit quantum circuit that implements the time evolution unitary using the stabilizer formalism. As an application of our construction, we introduce novel flow-based decompositions for known two-dimensional encodings, leading to circuit decompositions of time-evolution unitaries that are shallower than state-of-the-art approaches. We generally observe a space-time trade-off, where mappings with larger qubit-to-fermion ratios tend to yield shallower time-evolution quantum circuits.