As software systems grow in complexity, scale, and update frequency, parallel fuzzing has become essential for mitigating the efficiency limitations of traditional fuzzing. Effective task allocation is vital in maximizing parallel fuzzing efficiency and has garnered significant attention. However, current strategies often neglect critical code areas, treating all regions uniformly and resulting in suboptimal exploration. To address the limitations of current approaches, we present FlexFuzz, a novel parallel fuzzing system. First, we identify the boundary basic blocks that connect covered and uncovered areas, dynamically adapting them as fuzzing progresses. Second, we introduce a boundary-sensitive task allocation scheme that assigns fuzzing tasks based on the identified boundary basic blocks and their potential for exploration. Finally, to ensure focused exploration, we implement a multi-target, distance-guided approach that directs each instance to concentrate on its relevant task area. We have implemented a prototype of FlexFuzz and comprehensively evaluated it against the state-of-the-art parallel fuzzing systems. Across standard benchmarks, FlexFuzz surpasses other parallel tools: it increases coverage by 20.09% over the next best tool (PAFL), and identifies 33.75% more vulnerabilities than the next best tool (AFL++).