You will not get any avios back if cancelled within 24hrs of departure.
Unfortunately I know this the hard way from once a few years ago (before smartphones) when I wanted to cancel something 26hrs before departure, but the U.S. (where I was) and UK offices were closed until 22hrs before departure so I couldn't get hold of them to cancel. [I had no internet access in the remote place I was staying and only had the U.S. and UK numbers at hand]
You will get back any taxes exceeding the cancellation fee - usually only applicable on longhaul routes with carriers with high YQ (so not AA or CX).