Answer:
Mr. Johnson always takes the day off on Flag Day, which is celebrated in June.
Step-by-step explanation:
Because "Flag Day" is the title of the day, instead of "the flag day" or "a flag day", it makes it a proper noun and thus you would capitalize the entire title of the day. For example, you would write other holidays such as Mother's Day in sentences such as "The family went out to dinner on Mother's Day.", because "Mother's Day" is the title of the day itself.
June is also a proper noun, it being the name of a month, and thus you would also capitalize it.