OK, this is how it goes. DDD grabs you, and starts the chain grab. You slide down the stage and he runs towards you. From here, DDD will do a follow up attack, and you dont even have a full second to do anything. So, getting in the air, is out of the question, so no zair. You can either spot dodge, shield, or do the AAA combo. If you get DDD with the first hit of the AAA combo, he will flinch, and you can continue or do whatever you want. Now, sometimes his super armor from the grab does happen, but in this case, he was gonna get you with the grab unless you chose the spot dodge option. So thats where the mind games come in. If DDD notices your spot dodges, he will probably do a dash attack since the trip has a delay to it. Or DDD will just extend his hammer (his forward B attack I think). If he does the the dash attack, your AAA combo will work. There's other mind game scenarios that could happen as well, and i dont feel like explaining them all. I'm just saying that zair, will not work in the middle of a chain grab. In the middle of Falco's chaingrab, maybe, but thats a different story.
Note: These scenarios only work IF the DDD's timing is off. Other than that, they will just chain grab you without you being able to get out.