Code isn't mine! All credit to vincestyling on StackOverlow in this question: http://stackoverflow.com/questions/25258311/how-do-i-get-inpustream-as-response-in-volley-library
It's surprisingly difficult to get responses from Volley as an InputStream. Some people needed this for message pack encoding, I needed it to get an image response as an InputStream so I could do a multipart upload to another URL. I've since come across the loopj HTTP library and use that instead for my usecase as it's much simpler.
The relevant commit with Volley edits is here: https://github.com/georgiecasey/android-volley-inputstream-as-response/commit/62d9b9132c4f66b2268e9099d418b28884c26ce5
An example usage Activity is in src/com/georgiecasey/inputstreamresponseexampleusage/ExampleUsage.java