No. You win by revealing every safe cell. Flags are only notes for yourself and make no difference to whether the game counts as won.
You do not need a single flag to win. The game is won the moment every cell that is not a mine has been revealed.
What flags are for
A flag is a reminder that you think a cell hides a mine. It stops you from clicking that cell by accident: a flagged cell cannot be revealed until you take the flag off (how to flag a mine).
Wrong flags don't lose the game
A flag on a safe cell costs you nothing by itself, but you will have to remove it before you can reveal that cell. The game is only lost by revealing a mine.
Do flags help?
Most players flag the mines they have worked out, because it keeps the mine counter useful and makes numbers easier to read. The Minesweeper tips guide explains when flagging helps. See also how to play Minesweeper.