This is the kind of mistake that makes me judgmental, because I can’t fathom why people get it wrong. I sometimes see unnecessary apostrophes on a plural word ending in a vowel (like pajamas) or acronym (like CDs), because some people (wrongly) think you can’t pluralize those words without it. But what on earth would make you think the plural of “shot” needs an apostrophe?
There’s about a 1% chance the person who authored this sign meant “The flu shot’s here” and just dropped that initial “the.” But that would be oddly grandiose. Just ditch the apostrophe, dude.
p.s. I never get a flu shot. Am I tempting fate?