A flunky is someone who works obediently for another person. You might apply for a job as a personal assistant, only to realize during the interview that it's really a job as a flunky.
A flunky's job is to do whatever he or she is told to do, preferably without question, in a docile, dutiful way. A mob boss or other criminal mastermind might send flunkies out to do his dirty work, while in the old days a typical flunky was a footman or butler — a servant. This meaning comes from the Scottish flunkey, meaning "footman or liveried servant."