The USB connection is a digital one and is only used for data transfer.
The aircraft intercom audio is in an analogue format. To record it, you would need to connect the output to the external audio input on your camera. Normally this is a small 3.5mm socket.
What you would need to do is 'split' the intercom output (the 6.35mm stereo jack you connect your headphones to) to two outputs. One to go to your headphones, the other to feed into your camera.
6.35MM 1/4" PLUG TO 2 x JACK SOCKET HEADPHONE SPLITTER ADAPTER STEREO CABLE/LEAD | eBay
The above cable would do that for you, giving you two 6.35mm sockets. You can connect your headphones to one of those. However, as your camera is likely to use 3.5mm as opposed to 6.35mm plugs, you need an adapter like this to go into the second socket:
6.35mm to 3.5mm stereo Adapter 3-6M3F £0.25
You can't connect your camera directly into that though, as the aircraft intercom uses a 'line level' output signal. The camera (unless it's an incredibly expensive model) is likely only able to accept 'mic level' inputs. These are far lower levels and attempting to hook up the intercom directly will result in horribly distorted audio. You need to step down the output by using an attenuation cable like the following:
Sescom LN2MIC-35DB-3 3.5 Line to Mic 35dB Att. 3Ft DSLR Cable for Tascam DR-10
That cable has two male 3.5mm plugs, one goes into the above adapter, the other into your camera. That should allow you to record whatever is on the intercom.
The above is only an example of how you may do it, but the key points are that you will need some sort of splitter to get multiple outputs, an adapter to go from 6.35mm stereo to 3.5mm, and some sort of attenuation.
Don't forget also when getting a splitter, you need something that takes a stereo output and splits it into two more stereo outputs (TRS or 'tip-ring-sleeve' connectors). Some cables take the stereo output and split the channels into two mono output (TS or 'tip-sleeve' connectors).
I can't remember the exact allocation of channels with aircraft intercoms but I'm pretty sure you need both.
A much simpler way of doing this would be to simply purchase a little lapel type mic, with a 3.5mm stereo plug, connect that to your camera and put the mic inside an earcup of your headphones. That way you will record whatever it is you hear, which will be a mix of the aircraft intercom and the ambient noise. That's far more desirable IMO. Although it can occasionally get a bit uncomfortable having a small mic loose in your ear and if it starts moving about will affect the quality of the audio.
Hope that helps!