DIAGNOSIS Coil whine from the internal power regulation circuitry. It is caused by electrical interference or a poor-quality power supply creating audible frequency vibrations.
FIX Isolate and replace the power source. Step 1: Unplug the USB power cable from the Fire Stick's micro-USB port. Listen. If the noise stops, the issue is downstream. Step 2: Replace the power adapter. Do not use the TV's USB port. Use only the included Amazon power adapter plugged directly into a wall outlet. Step 3: If using the included USB cable, try a different, high-quality USB cable. A poor cable can cause voltage instability.
IF THAT DIDN'T WORK The noise may be induced through the HDMI connection. Insert a passive HDMI coupler or a short HDMI extension cable between the stick and the TV port. This can break the ground loop that may be transmitting the sound.
HEADS UP This is generally not a sign of imminent failure, but an annoyance. If the noise persists with a known-good wall adapter and cable, the whine is internal to the stick. Contact Amazon support, as this can be a defect covered under warranty.