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Say I attack with Optimus Prime - Battlefield Legend with a Rapid Conversion in my hand and flip a Brainstorm for the attack. If I play the Brainstorm and play the Rapid Conversion from hand to target Optimus, am I able to play the action that he retrieves from the graveyard as the second action for Brainstorm?

No. You must fully resolve Brainstorm before the ability from his flip triggers.
Source: Wizards of the Coast (2019-02-18)    【Link to Ruling】
Tags: Brainstorm, Brainstorm