Most dampers are designed to close DOWN, and are kept closed by the weight of the damper. Get a pair of safety glasses and a flashlight, check for foreign material or mortar that may be keeping the damper from seating, and that the metal of the damper plate is not warped.
Sweveral possible problems- lack of draft (damper closed, chimney blocked) lack of combstion air, wet wood, wrong wood. Find a competent chimney sweep or chimney specialist, and have them check it.
In the event of fire, the fusible link melts and the shutter gets closed. This helps in blocking the fire from spreading through the duct ----- If you are asking about a damper on a stove or chimney, that is not called a fire damper, but just a damper. There is a link to a question on that below.
It's important that an indoor fireplace flue damper be opened before igniting anything in a fireplace. The damper looks similar to a trap door and is located at the bottom of the chimney. When it's open, it provides an opening for smoke from the fireplace to escape. If it is closed while a fire is lit, smoke will enter the room rather than leave via the chimney with possible deadly consequences. If nothing is burning in the fireplace, keep the flue damper closed. This saves money on energy by preventing heat or air conditioning loss up through the chimney.
Dampers are usually arranged to close DOWN, so that the weight of the damper keeps it closed. Use a flashlight- it helps to see what you are doing in that very dark place.
A top damper or cap damper is a metal spring door placed at the top of the chimney with a long metal chain that allows one to open and close the damper from the fire place.
Virgie M. Ammons of Eglon, West Virginia"Inside the fireplace chimney is a device called a "Damper". The damper is opened and closed to allow smoke from the fireplace to be drawn upward out of the house. The "Fireplace Damper Actuating Tool" designed by Ammons allows the damper to be"locked" in the closed position, preventing cold air and dust from blowing down the chimney back into the house."Patent No. 3,908,633 September 30, 1975 Source: Black Facts Online
One can purchase a chimney damper from a variety of stores. Chimney dampers can be purchased from fireplace specialists such as Woodland Direct, or from online stores such as Amazon.
Something is preventing your fireplace from drawing. The damper may be closed, or partially closed. Your chimney may have a blockage, or you may have prevailing winds that push smoke back down the chimney. If you have air flow problems, such as a vent fan that draws air out of the house, it can cause that. Bottom line- if the damper is open, and the flue is not blocked, you need a good fireplace/chimney specialist to examine what you have.
When you use the fireplace, the damper should be open all the way. If not, you probably will not get enough updraft and your house will fill up with smoke...not a good thing. When it is not in use, the damper should be closed...otherwise you will lose a lot of heat up the chimney.
By flue, I believe you mean the damper in the chimney, which has the effect of closing off the flue. Close the damper any time you are not using the fireplace. Remember -heat rises -so heated air will also rise up and out the flue in the winter. In the summer it is also good to keep the flue closed because heat and humidity will activate the smelly properties of the ash and creosote in the firepalce chimney and create a bad odor in the home. In order for a damper to do its job it must seal tightly/ If your existing mechanical damper is broken, missing or in a bad state you can repair it or replace it with a chimney top damper or a chimney balloon. But, open the damper before lighting a a fire, or it will rapidly get quite smokey in the house.
fireplace
Put on a pair of safety glasses or goggles (you ARE going to get stuff in your face) get a good flashlight, and get a look at the damper. Most are hinged, and will swing UP the chimney. Most have a bracket and support the holds it open or closed. With the light to help you see, move the support so that it is free of the bracket, and try to swing it open (up). If it does not move, you may have foreign material in the chimney (especially if your chimney does not have a cap). If that is the case, you need the services of a chimney sweep.