The rapid advancement of generative artificial intelligence has spurred innovative approaches to semantic communication, giving rise to a new paradigm known as generative semantic communication (GSC). The integration of flexible cross-modal semantic extraction with generative capability-driven semantic inference substantially enhances semantic compression efficiency, demonstrating significant promise under communication resource constraints. Nonetheless, the stringent dependence on high computational power and the resulting latency continue to present major challenges, thereby limiting the feasibility of large-scale deployment. To address these challenges, we propose a novel GSC framework named FAST, which stands for flexible and adaptive semantic transmission. To accommodate limited computational resources, we propose a sequential semantic extraction method, where a temporal prompt engineering module orchestrates the distillation and transmission of key semantic units. Correspondingly, we introduce a sequential conditional denoising module at the receiver, which adapts the diffusion-based reconstruction to the progressively received input. To enhance overall task performance in multi-user semantic transmission, we propose a semantic-aware resource allocation method that optimizes bandwidth dynamically based on a joint consideration of semantic dependencies, user-level task priorities, and instantaneous channel conditions. Extensive experiments demonstrate that the proposed architecture achieves system precision comparable to conventional GSC systems while significantly reducing transmission latency and improving overall efficiency. These results confirm its enhanced potential for deployment in multi-user GSC scenarios with stringent communication and computational constraints.