The last decade has witnessed a huge increase in data being ingested into the cloud, in forms such as JSON, CSV, and binary formats. Traditionally, data is either ingested into storage in raw form, indexed ad-hoc using range indices, or cooked into analytics-friendly columnar formats. None of these solutions is able to handle modern requirements on storage: making the data available immediately for ad-hoc and streaming queries while ingesting at extremely high throughputs. This paper builds on recent advances in parsing and indexing techniques to propose FishStore, a concurrent latch-free storage layer for data with flexible schema, based on multi-chain hash indexing of dynamically registered predicated subsets of data. We find predicated subset hashing to be a powerful primitive that supports a broad range of queries on ingested data and admits a high-performance concurrent implementation. Our detailed evaluation on real datasets and queries shows that FishStore can handle a wide range of workloads and can ingest and retrieve data at an order of magnitude lower cost than state-of-the-art alternatives.