Solar thermal technologies have great potential to provide low-cost storage for solar energy. However, their efficiencies are limited by a lack of scalable, mechanically flexible, durable, yet highly-efficient spectrally-selective solar absorbers suitable for high temperatures at low solar concentrations. Here, we overcome these challenges by fabricating a scalable free-standing spectrally-selective thin-film Si absorber and emitter (SSTFS) composite. Its high-temperature emittance shows strong spectral selectivity, even at 595 °C. Thermal stability is proven by measuring optical properties before and after thermal cycling equivalent to one day of concentrated sunlight. Despite the use of crystalline Si, the fabricated SSTFS composite exhibits exceptional mechanical flexibility to cover most surface geometries. The SSTFS composite demonstrates the potential of high-temperature, efficient and flexible solar absorbers and thermal emitters to advance renewable solar energy with storage.