Resistor values for a passive audio mixer?
I'll assume this is not actually for use in an aircraft- if you are actually mucking with stuff in the cockpit, see your DAR for official advice that conforms to FAA etc. airworthiness requirements.  

If you use 10 ohm resistors and the impedance of the phones is really 10 ohms (often that's pretty variable) your av audio power will be reduced by about 12dB, which is quite a bit. Also the headphone impedance your MP3 player is expecting is typically more like 35 ohms. 

I would suggest trying more like 27 ohms on each MP3 output and 5.1 ohms on the av output. That will reduce the av power by less than 6dB. The MP3 sound may not be loud enough, but it's probably not really designed to drive a 10 ohm headset.