Before wiring anything, you need to see if the OTG cable even gives you power. If it does not, all this work is for nothing.
Even a cheap meter will help you better understand what is going on.
USB cables have power on the outer edges on the normal PC style plug that most of these OTG cables become. The issue here is if the device has to negotiate before allowing power or not. I do not use OTG so have never looked into it.
To get your self started maybe you should take power from a normal usb port(very carefully, do not use the data pins, just keep then from touching anything and tape them off separately).
Take the Black wire and connect it to the LED's cathode end(on a normal led it has a shorter pin and is the longer side inside the led, but you may not be able to see that on this setup). Connect the resistor(for 5 volts lets use 120-200 ohms or so to limit yourself to 15-20ma current flow) to the other lead on the LED(anode) and the other end of the resistor to the red wire. With a meter you can be 100% sure what you are connecting by pre checking the power.
If all is good this will allow a computer usb port to light your led.
Please note starting with a large resistor(I have a 5k 1 turn variable that allows better control to find just how much light I would want. It was picked up for something else, but works for this as well) and working down is a good way to fine tune the brightness.
I can not offer you a simple yes or no answer on how to connect to your device because I do not own the device and they do not make the specs available to the general public. The mic wire may have 5 volts or only 1.5. I have no way to tell and again current limits are another issue.
This is a writeup that has some info on how the OTG setup works. You will quickly see that without being designed for it, chances are it will not work for your application.
http://www.ti.com/lit/wp/sszy001/sszy001.pdf