I'm confused. The flue, as I understand it, is the damper that closes off the vent that goes up the chimney. It is typically made of metal, probably cast iron.

If yours is made of tiles and has a cracked tile, the problem would be that, when you want to close off the chimney, when you do not use the fireplace, you cannot close it off all together. In cold weather, you would feel a draft, and you would be losing heat. That would be as bad as having a door that does not seal properly. Similarly, in warm weather, you would be losing air conditioned air, if you have air conditioning.

Do I understand you correctly?