It is well known that superradiant decay of an ensemble of N spins generates a complex non-classical state of light. Here, we consider the estimation of a phase encoded in the initial spin state from a superradiant burst of photons: how is information about this phase distributed among the emitted photons, and can the phase be estimated using simple measurements? Despite the complexity of the photonic burst state, we show that a simple homodyne measurement combined with an optimized filter and linear estimator recovers the N-scaling of the quantum Fisher information of the initial spin state (including cases exhibiting N^2 Heisenberg scaling). Even more surprising, the temporal mode with optimal information content contains a vanishing fraction of the total emitted photons in the large-N limit, suggesting an effective compression of phase information. Our results and setup represent a new approach to quantum metrology for spin systems, in that they enable cavity-based readout of solid-state spin ensembles that utilizes resonant spin-photon interactions.