Achieving Bloch oscillations of free carriers under a direct current, a long-sought-after collective many-body behavior, has been challenging due to stringent constraints on the band properties. We argue that the flat bands in moiré graphene fulfill the basic requirements for observing Bloch oscillations, offering an appealing alternative to the stacked quantum wells used in previous work aiming to access this regime. Bloch-oscillating moiré superlattices emit a comblike spectrum of incommensurate frequencies, a property of interest for converting direct currents into high-frequency currents and developing broadband amplifiers in terahertz domain. The oscillations can be synchronized through coupling to an oscillator mode in a photonic or plasmonic resonator. Phase-coherent collective oscillations in the resonant regime provide a realization of current-pumped terahertz lasing.