When you speak of a flock, you are usually describing a group of people with a religious devotion, or those that follow a religious leader. Most often people would use the word congregation although flock is also acceptable.
Ex: When the vicar broke the news of his impending retirement to his flock, they were devastated and asked him to reconsider his decision.
Ex: The clergyman was very proud of the gift he had received from his former flock, a leather¬bound copy of the Bible with an insert signed by each congregant.
A flock can also refer to a group of animals, such as a flock of sheep, goats, or birds.
Ex: When the shepherd attempted to leave the hut, a flock of lambs were waiting to meet him and be taken out to graze.
Ex: The mother duck, followed by her flock of ducklings, made her way out to the middle of the pond where she began to teach them to look for food.
A mass of people is a large group of people. The word has a strong connection to anonymity, or being one member of the mass.
Ex: At the open-air concert, the mass of music fans was determined to stay no matter how the weather threatened their comfort.
Ex: A mass of fresh, but inexperienced troops mobilized for action on the border during the weeks leading to the war.
When someone refers to the masses, they often mean the large number of common people. Sometimes, the term the masses is used to imply the idea of a large number of people without inside knowledge or special privileges.
Ex: The party leader did not really care about the good of the masses, but he used their ignorance to his advantage and rallied their support for his candidacy.
Ex: Thought to be good enough only for the masses, dark, unrefined bread was considered inferior by European royalty of the 16th century.