Nikon D3300 Headphone output?
Microphone outputs are typically very low level and have only enough output to drive a sensitive preamp, not headphones.  To drive headphones you need an amplified output.  According to a variety of sources, the D3300 does not have a headphone jack, which means you have to provide a separate amplifier, which means you have to provide one, and the power to drive it, and the cable to connect to it.  I suspect the best solution would be a battery-powered preamp that receives your mic output and then delivers two amplified outputs: line level for your D3300 input jack and phones-level for your headphones.