With the advent of wearable microelectronic devices in the interdisciplinary bio-electronics research field, synaptic devices with capability of neuromorphic computing are attracting more and more attention as the building blocks for the next generation computing structure. Conventional flash-like synaptic transistors are built on rigid solid-state substrates, and the inorganic materials and the high-temperature processing steps have severely limited their applications in various flexible electronic devices and systems. Here, flexible organic flash-like synaptic devices have been fabricated on a flexible substrate with the organic C8-BTBT as the conducting channel. The device exhibits a memory window greater than 20 V and excellent synaptic functions including short/long-term synaptic plasticity and spike-timing-dependent plasticity. In addition, even under the bending condition (7 mm bending radius), the transistor can still stably achieve a variety of synaptic functions. This work shows that low-temperature processing technology with the integration of organic materials can pave a promising pathway for the realization of flexible synaptic systems and the future development of wearable electronic devices.