Also a few others things I found:
mapping messed up on stand-alone Flash player app (latest version) too on OSX Mountain Lion.
on OSX El Capitan (the newer version of OSX on which I tested the Firefox and Safari versions that don't detect the gamepad), the stand-alone Flash player app doesn't detect gamepad at all.
sometimes, even on Chrome, where the mapping works fine, I have to press a button or move a stick for the gamepad to get detected. This is not ideal, because if the user has a gamepad connected, they won't know the game supports it unless they actually try to use the gamepad first. To check if a gamepad is connected, I'm checking that FlxG.gamepads.lastActive != null.