1. Firmware of commercial devices is not open source. That is the factory firmware in the normal way to get it is almost unreal
2. Firmware commercially sold devices (and not engineering, which are testing and check your solution the developers) is different from what happens in normal development. For example, you may not be soldered legs to connect the programmer, the chip can be sewn separately from the device, and then do on the Board may not be release or even the entire controller (uart or something similar).
3. Even if the Board has all the firmware can usually be zamochennoy from flashing.
Poet you probably have only two ways -
1. To try to find in the Internet the instructions for hacking your specific model of headphones, if someone is still hacked and posted on the web. Usually headphones few deals.
2. If you know anything about audio, maybe you can develop your own electronics based on another programmable device, and can replace the original stuffing their own development.