Controlled obtaining of orbital angular momentum (OAM) modes of light at high power over arbitrary orders has important implications for future classical and quantum systems. Appreciable optical amplification has recently been observed for low-order or specific-order OAM modes. However, large amplification of high-order OAM modes still remains challenging. Here we report on flat-gain amplification of arbitrary OAM modes via Brillouin interactions and demonstrate that the OAM modes with various orders can be efficiently and relatively uniformly amplified by imaging the wave source of OAM mode propagation in a nonlinear medium. Meanwhile, the propagation properties of beams carrying OAM with arbitrary modes are high-fidelity maintained. This work provides a practicable way to flatten the mode gain and represents a crucial necessity to realize OAM mode filters with controllable mode gain bandwidth.