This is the flag of the Pope and the Vatican City, and been used by both for over 75 years. It features a yellow and white field, with the Papal Coat of Arms on the white field. The emblem also consists of the silver and gold keys of Saint Peter and a red thread that binds them. Finally topped off with the triple tiara of the Pope. It is flown to represent the sovereignty of the Pope and the Roman Catholic Church, for the Vatican City and the Holy See.
If this is the flag you’re looking for, but you want a more formal flag check out the Papal Ceremonial Flag Set.