The emergence of large-scale order in self-organized systems relies on local interactions between individual components. During bacterial cell division, FtsZ -- a prokaryotic homologue of the eukaryotic protein tubulin -- polymerizes into treadmilling filaments that further organize into a cytoskeletal ring. In vitro, FtsZ filaments can form dynamic chiral assemblies. However, how the active and passive properties of individual filaments relate to these large-scale self-organized structures remains poorly understood. Here, we connect single filament properties with the mesoscopic scale by combining minimal active matter simulations and biochemical reconstitution experiments. We show that density and flexibility of active chiral filaments define their global order. At intermediate densities, curved, flexible filaments organize into chiral rings and polar bands. An effectively nematic organization dominates for high densities and for straight, mutant filaments with increased rigidity. Our predicted phase diagram captures these features quantitatively, demonstrating how the flexibility, density and chirality of active filaments affect their collective behaviour. Our findings shed light on the fundamental properties of active chiral matter and explain how treadmilling FtsZ filaments organize during bacterial cell division.