Yes, many of our fireplaces are safe to use with flat TV screens. You need to check whether your fire is "closed" at the top to assess suitability. Some of the new wall-hanging units are open at the top and have a glass panel at the front. They are NOT suitable to be put underneath TV because all the heat goes up, so it would damage your TV.
If the distance between the fireplace and the TV is fairly small, you may recess either the fireplace (lining the top of the recess with a solid fireproof material) or the TV, making at the same time a sort of a heat absorbing "shelf" between the fire and the TV.