Where in the Constitution does it state that filibusters are legal?

There is no mention of a filibuster in the Constitution either permitting or prohibiting it. It is implicit in the idea that the Constitution places no time limit on how long a Congressman may speak on an issue. Congressmen have the right to speak in support of or against any particular bill without a limit on the time unless that house of Congress imposes one. The Constitution in Article 1 gives each house the power to make its own rules of order. While now there is no time limit either house does have the power to impose such a limit if it chooses to. Sometimes if it looks like the minority party is starting a filibuster, the other party makes a motion to limit the time for debate on that bill in order to break the filibuster.