Step 1: List the incubation windows side by side: influenza 1 to 3 days, measles 10 to 14 days, chicken pox 2 to 3 weeks, rubella 2 to 3 weeks.
Step 2: Pick the minimum. Influenza, a respiratory virus that spreads explosively, has by far the briefest interval before symptoms appear.
Step 3: The three rash-producing infections all incubate for about two weeks or longer, so they are ruled out as the shortest.
\[\boxed{\text{Influenza}}\]