In The Untouchables (1987) a reporter takes a picture of Elliot Ness as he's smashing a box presumably full of illegal liquor, then about thirty seconds later, takes another photograph of Ness looking like an idiot while holding a novelty umbrella that was actually in the shipment instead of booze.
My question: would it be possible for the reporter to take two photos in such quick succession using a 1930s era flashbulb camera?
Yes. Even cameras that shot on sheet film like the speed graphic camera could b shot in quick succession by a well trained photographer. If sheets of film were being shot you placed the sheets of film into a film holder, before making the shot you would remove a cover on the film holder and make your exposure. Then afterwards, you'd place the cover back over the film and you would flip the holder around (to take shot #2). Special holders existed that could hold multiple sheets of film in one holder, so if he was using a holder like that it would make it easier. Also, the man in the movie might have been using a roll film holder so he could easily get multiple shots done in quick succession. In the case of this film I imagine the photographer would have done the same and then changed out his flash bulb and taken another shot. Cameras like the graphics were quite common for a long time for press photography. Although smaller 35mm cameras eventually won out due to ease of use, there were still photographers using them professionally to cover events into modern times.