So I bring in a WAV file into the timeline on Flash Pro CS6 and into a new layer. As I hit play to test if the audio works, it works just fine. However, when I pause the audio in the middle of playing and I resume it, I don't hear it anymore. I'm not sure what's the problem with it but I just want to hear the voice recording, which is the audio I was talking about, resume after paused in the middle of it. Thanks
Your audio's Sync setting must be set to Event type. It should be changed to Stream type if you wish to play and stop it from anywhere in sync with the Timeline playhead.
Select the Timeline frame having the audio and open Properties Panel. Over there change the Sync setting to Stream and then try.