I tried it just like you and I had the same results. I looked into the PyAudio installation instructions to see if I was missing something, nevertheless I was not able to find anything. According to the make output the PortAudio package, it was successfully installed. I'm not sure what's the root this behavior, but it may be related to the PortAudio installation directory. Anyways, I suggest you to contact PortAudio, they may be able to provide you a more accurate answer of why this is happening.
I will followup if I find any solutions.
Hi I was able to first install port audio by sending it to the Edison and then I was able to install pyaudio with pip .
I hope this works for you too.