We demonstrate a single-stage all-fiber nanosecond amplifier with a total average power of greater than 1.4 kW by employing what we believe to be a novel multi-cavity passively Q-switched fiber laser as the seed laser. The multi-cavity seed laser adopts a piece of Yb-doped fiber (YDF) as saturable absorber (SA), and it includes two external cavities resonating at 1030 nm and an internal cavity working at 1064 nm, respectively. Using such a scheme, a stable dual-channel laser output with a total average power of >35 W, a pulse width of 45 ns, and an optical conversion efficiency of 72% operating at 1064 nm is achieved. By power scaling the multi-cavity seed laser, a dual-channel single-stage nanosecond amplifier is obtained with a single-port average power of exceeding 700 W and a pulse energy of about 7.3 mJ. To the best of our knowledge, this work is the highest average power and optical conversion efficiency for passively Q-switched all-fiber laser employing SA fiber, and the highest average power for a single-stage all-fiber nanosecond amplifier.