How to amplify a 3.5mm headphone analog signal?
You should understand how the microphone input of the phone works, first.  Here's a good article:

http://www.openmusiclabs.com/learning/sensors/electret-microphones/

Note that the microphone port provides a tiny bit of power to the microphone. Honestly this isn't a lot of current, and it's meant simply to operate the JFET inside the microphone capsule.

If you can, you should install a battery in your project and use a typical amplifier setup, which then leads to the microphone port of the phone.  

Beyond adding a battery, what I'm suggesting is that you may be able to subvert this current and use it to power an amplifier circuit. If you measure the current available under different loads (just measure the voltage and current across a variety of resistors, graph it, and it'll tell you how much power is actually available for your use.

Once you know the voltage and current you'll be running at, you can attach a regulator to the microphone port, filter the output of that, and power a simple opamp electret microphone amplifier with it.  The output of the opamp then goes back through a capacitor to the microphone port (which is the opamp's power supply source).

You're going to have a lot of side effects doing it this way, but it may give you enough headroom in your signal to succeed in your project.

I still think a stethoscope style pickup is a better option, though.