We present FLASH-TB, a journey planning algorithm for public transit networks that combines Trip-Based Public Transit Routing (TB) with the Arc-Flags speedup technique. The basic idea is simple: The network is partitioned into a configurable number of cells. For each cell and each possible transfer between two vehicles, the algorithm precomputes a flag that indicates whether the transfer is required to reach the cell. During a query, only flagged transfers are explored. Our algorithm improves upon previous attempts to apply Arc-Flags to public transit networks, which saw limited success due to conflicting rules for pruning the search space. We show that these rules can be reconciled while still producing correct results. Because the number of cells is configurable, FLASH-TB offers a tradeoff between query time and memory consumption. It is significantly more space-efficient than existing techniques with a comparable preprocessing time, which store generalized shortest-path trees: to match their query performance, it requires up to two orders of magnitude less memory. The fastest configuration of FLASH-TB achieves a speedup of more than two orders of magnitude over TB, offering sub-millisecond query times even on large countrywide networks.