The Q can be said to stand for Queer or Questioning, or both. “Queer” is more of a blanket term for people who belong to the LGBTQ+ community or who identify as something other than heterosexual or cisgender (a term that has come to describe people who feel that their gender does fall in line with their biological sex; i.e. someone born male feels that he is a man). Questioning means exactly what it sounds like: it gives a nod to those who are unsure about their sexuality and/or gender identity or who are currently in the process of exploring it.
There’s no one flag specifically for the letter Q, as all of the above sexualities and identities technically fall underneath this term.