NVMe zoned namespace (ZNS) SSDs present a new class of storage devices with attractive features including low cost, software definability, and stable performance. However, one primary culprit that hinders the adoption of ZNS is the high garbage collection (GC) overhead it brings to host software. The ZNS interface divides the logical address space into size-fixed zones that must be written sequentially. Despite being friendly to flash memory, ZNS requires host software to perform out-of-place updates and GC on individual zones. Current ZNS SSDs typically employ a large zone size (e.g., of GBs) to be conducive to die-level RAID protection on flash memory. This impedes flexible data placement, such as mixing data with different lifetimes in the same zone, and incurs sizable data migrations during zone GC. To address this problem, we propose FlexZNS, a novel ZNS SSD design that provides reliable zoned storage allowing host software to configure the zone size flexibly as well as multiple zone sizes. The size variability of zones poses two interrelated challenges, one for the SSD controller to establish per-zone RAID protection, and the other for host software to manage variable zone capacity loss caused by parity storage. To tackle the challenges, FlexZNS decouples the storage of parity from individual zones on flash memory and hides the zone capacity loss from the host software. We verify FlexZNS on a ZNS-compatible file system F2FS and a popular key-value store RocksDB. Extensive experiments demonstrate that FlexZNS can significantly improve the system performance and reduce GC-induced write amplification, compared with a conventional ZNS SSD with large-sized zones.