Did Hezbollah ever have a flag with a nuclear mushroom cloud on it?
Hezbollah has used a variety of symbols, but there is no evidence that they have officially adopted any that relates to nuclear weapons. Christopher Hitchens does indeed use the words "party symbol" in the video, but that's probably a slip of the tongue. What he had in mind was a random banner in one rally (Dahiyeh, Beirut, 2009):
A huge poster of a nuclear mushroom cloud surmounts the scene, with the inscription oh zionists, if you want this type of war then so be it! During the warm-up, an onstage Muslim Milli Vanilli orchestra and choir lip-synchs badly to a repetitive, robotic music video that shows lurid scenes of martyrdom and warfare.
Source: The Swastika and the Cedar, Christopher Hitchens, Vanity Fair.
James Kirchick also attended the event, and gives a similar description of the banner:
A giant banner on the back wall bore the words, “Oh Zionists, Oh Zionists, if you want this type of war, SO BE IT,” surrounding Arabic calligraphy bearing the same message in the form of a mushroom cloud.
Source: Lebanon on Tenterhooks, James Kirchick
Hezbollah's use of aggressive, chest pounding symbolism is no secret, but calling the banner "official party symbol" is a stretch. It never appeared in any official Hezbollah documentation and it hasn't made any notable reappearance in any form since that event.
Mr. Rushdie's claim is far too vague to investigate.