The limitations outlined in Milliway's answer stand (the power supply itself, additional peripherals for the Pi, volume level of the amplifier). For the Pi 3 and its Polyfuse it is reasonable to expect it to work if no other high current peripherals are connected to the Pi. From the question and comments I take it that the Pi and the amplifier should be powered from a single USB power bank. This restriction alone however does not necessarily require the amplifier to be connected via the Pi. A simple wiring could connect both the Pi and the amplifier in parallel directly to the power source - avoiding to channel the amplifiers power through the Pi.
Here we find some numbers for a 50,000mAh power bank and a Pi2B.
According to actual Raspberry Pi Power Measurements the Raspberry Pi Model 2B consumes about 350 mA when shooting 1080p video. Let's play it (very) safe and double that amount, and convert it into watts to compute the running time:
2 * 350 mA * 5 V = 3.5 W
A 50 Ah power bank usually has a capacity of about
50 Ah * 3.7 V = 185 Wh
Note that the mAh rating of a power bank typically refers to its internal cell voltage of 3.7 volts, not to its output voltage of 5 volts. You can then expect your Pi to run for
185 Wh / 3.5 W = about 53 h, or more than 2 entire days
Filling in 750 mA as an expected maximum for a Pi 3 (see here) we get approx. 3.75 W for the Pi. Add your 3.7 W for the amplifier to the 3.75 W for the Pi and get something along:
185 Wh / 7.2 W = about 25 h
The real live performance might be very different due to various external factors (e.g. conversion efficiency of the power banks step-up converter, battery fatigue, and all the issues listed in the beginning of this post).