I drilled a hole in the fireplace flue
First of all, yes the condition is dangerous.  You have compromised the integrity of a part designed to protect you from smoke and toxic gasses that are released by combustion.  Released into a relatively confined spaces these bad gasses can accumulate and pose health hazards.  Carbon dioxide and carbon monoxide are your primary concerns here.

But you haven't put the people below you in any danger.  You've put yourself in danger.  The gasses will be releasing into your unit, not theirs.

Since this is an apartment you should first notify your landlord of the issue.  You will be responsible for the repairs, so you can offer to fix it yourself, but your landlord has the right to know of the damage and risk and you have a legal and ethical obligation to inform him.

For repairs, you'll need to open up the wall to get access to the flue.  Then you can patch the small hole with metal (MUST BE METAL) tape - this is available at most box stores and is specifically designed for sealing metal ductwork.