Do you verbs the fasten to embark on a fireplace flue? Or do you permit the fasten move about slack? I want to use the fireplace.

I don't feel a draft from the fireplace even if the fasten is pulled, or if the chain is disappeared loose...
Answers:    Not all damper mechanism operate in equal manner.
The "chain-pull" usually open a counter-balanced damper and the chain wants to be "latched" on to some type of cleat that holds the chain.

Use a flashlight to look up into the chimney crack to see what can be verified.

I would light some incense and determine if [pulled -chain position] the smoke escapes or is "drawn " up the chimney.
Perhaps even a few sticks/cones to increase the volume of smoke would be more describing.

If unsure it might be time to call a chimney sweep to inspect the machine.
it should open when you agree to the chain loose it could be stuck.if the fire place have not been cleaned contained by a few years you need to send for someone to clean it. the build up on the inside can burn your house down.