As indicated on the datasheet, you need to provide a DC power source for the microphone to operate. This comes down to the pinout of the mic connector. There probably is a standard within the aviation audio world. If you find it and post it, we can go from there. The 400 mV output should be enough to drive PC speakers that have a small power amp built in.
Separate from that, the LM386 is a small speaker amp chip. While there are modules on ebay that use it as a mic preamp, the chip is a very poor choice for that due to excessive noise (at microphone signal levels), distortion, etc. It is attractive because it has lotsa gain, needs very few external components, and biases itself internally for operation with a single power supply.
ak