Neuromorphic computing is of great interest among researchers interested in overcoming the von Neumann computing bottleneck. A synaptic device, one of the key components to realize a neuromorphic system, has a weight that indicates the strength of the connection between two neurons, and updating this weight must have linear and symmetric characteristics. Especially, a transistor-type device has a gate terminal, separating the processes of reading and updating the conductivity, used as a synaptic weight to prevent sneak path current issues during synaptic operations. In this study, we fabricate a top-gated flash memory device based on two-dimensional (2D) materials, MoS2 and graphene, as a channel and a floating gate, respectively, and Al2O3 and HfO2 to increase the tunneling efficiency. We demonstrate the linear weight updates and repeatable characteristics of applying negative/positive pulses, and also emulate spike timing-dependent plasticity (STDP), one of the learning rules in a spiking neural network (SNN).