OK, well the way I think of it, it’s the transport moving - the AAA is riding on the transport.
You can use a transport in the combat movement phase to do an amphibious assault that has an AAA previously loaded on it (earlier turn) and you could be unloading the infantry in an amphibious assault and necessarily leaving the AAA gun on it, so that is how you could possibly be “moving” an AAA gun during the combat movement phase.
Transports can’t be used as fodder in sea battles, so that doesn’t really make sense. Again, a transport laden with an infantry and AAA gun (the AAA would have to have been previously loaded, and could not legally be loaded this turn) could be moved in the combat movement phase in order to amphibiously assault with the infantry.
Also, a transport could be moved in the combat movement phase in order to avoid combat with enemy surface warships that the transport was sharing a zone with at the beginning of the turn.