The spatiotemporal information plays crucial roles in a multi-agent system (MAS). However, for a highly dynamic and dense MAS in unknown environments, estimating its spatiotemporal states is a difficult problem. In this paper, we present BLAS: a wireless broadcast relative localization and clock synchronization system to address these challenges. Our BLAS system exploits a broadcast architecture, under which a MAS is categorized into parent agents that broadcast wireless packets and child agents that are passive receivers, to reduce the number of required packets among agents for relative localization and clock synchronization. We first propose an asynchronous broadcasting and passively receiving (ABPR) protocol. The protocol schedules the broadcast of parent agents using a distributed time division multiple access (D-TDMA) scheme and delivers inter-agent information used for joint relative localization and clock synchronization. We then present distributed state estimation approaches in parent and child agents that utilize the broadcast inter-agent information for joint estimation of spatiotemporal states. The simulations and real-world experiments based on ultra-wideband (UWB) illustrate that our proposed BLAS cannot only enable accurate, high-frequency and real-time estimation of relative position and clock parameters but also support theoretically an unlimited number of agents.