The LUX-ZEPLIN (LZ) experiment is searching for dark matter interactions in a liquid xenon time projection chamber (LXe-TPC). This article demonstrates how control of the flow state in the LXe-TPC enables the identification of pairs of sequential alpha-decays, which are used to map fluid flow and ion drift in the liquid target. The resulting transport model is used to tag ${}^{214}$Pb~ beta-decays, a leading background to dark matter signals in LZ. Temporally evolving volume selections, at a cost of 9.0% of exposure, target the decay of each ${}^{214}$Pb~ atom up to 81 minutes after production, resulting in (63_$\pm$6${}_{(stat)}$_$\pm$7${}_{(sys)}$)% identification of ${}^{214}$Pb~decays to ground state. We also demonstrate how flow-based tagging techniques enable a novel calibration side band that is concurrent with science data. Finally we report updated estimates of radon-chain charge branching fractions in liquid xenon, finding branching to ${}^{218}$Po${}^{+}$ at $0.49\pm 0.01$, ${}^{214}$Pb${}^{+}$ at $0.48\pm 0.12$, and ${}^{214}$Bi${}^{+}$ at $0.74\pm 0.05$, with a mean charged ion lifetime in the LZ TPC of $49\pm 4$ min.