An automatic does not need the flywheel effect because it has a torque converter, which performs the same energy storage function, so it's understandable that an automatic's corresponding part would not necessarily have the same name.
And flex plates do flex, in fact they have been known to flex so much that they crack. But I will admit I don't understand why. I don't believe it is to compensate for misalignment between the engine and transmission, because the front bushing in an automatic will wear long before a flex plate will flex. Perhaps it is to absorb front to back movements of the converter generated by the input shaft during shifting.