Hey my house was built in the 1940's I have two built in fireplaces measuring about 2' wide and about 12" deep however they don't have dampers and the flames just get sucked up without providing any heat to the home. Can this be corrected or a damper put in?

Ouch I'm a mason by trade. It really depends on some things. First of all it would be a custom made damper casted or welded steel. To get a damper in you really should take of the face and install damper and then a smoke shelf behind damper. The finish face needs to be min 7' down from the damper for the little smoke roll a damper creates. I have built a fireplace in a fireplace nut not the opposite way. Also since it is so old did you check the chimney. A chimney sweep has a chimney scan camera to check brick or flues to see if the stack is sound.
You can try to weld up a damper and drill into the insides of the fireplace and then weld damper to big pins. But if that lets loose in time maybe a fire hazard. Sorry for the news.
I think that's a Rutherford design fireplace.

Signed 21 boat

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You can buy/install a chimney top spring loaded cap that will act as a damper. There is a cable running down the inside of the chimney to the fire box to control the cap.

ballengerb1 might have a good idea it depends on the face of your fireplace. The "roll" the firebox is the key to this and that's also the reason for the up the chimney heat gone quick. Can you post a picture for me to see the slope and roll? I'm trying to picture it. The fireplace is flush ti the floor with brick in front and is it parged/plastered over that it built into the actual wall and above the opening it slopes back quick and disappears into the wall. Is this for the fire looks nice or is the heat more of and Issue?