Here, we have experimentally demonstrated the selection principle of the seed power in a narrow linewidth fiber amplifier seeded by fiber oscillator based on a pair of fiber Bragg gratings. During the study on the selection of seed power, the spectral instability of the amplifier is found when a low power seed with bad temporal characteristics is amplified. This phenomenon is thoroughly analyzed from seed itself and the influence of the amplifier. Increasing the seed power or isolating the backward light of amplifier could effectively eliminate the spectral instability. Based on this point, we optimize the seed power and utilize a band pass filter circulator to isolate the backward light and filter the Raman noise. Finally, a 4.2 kW narrow linewidth output power is achieved with signal to noise ratio of 35 dB, which has exceeded the value under the highest output power reported in this type of narrow linewidth fiber amplifiers. This work provides a solution for high power and high signal to noise ratio narrow-linewidth fiber amplifiers seeded by FBGs-based fiber oscillator.