Connecting dryer duct to another duct
#1
Retail duct tape should never be used for ducts. As you have found it is temporary at best. Are these metal ducts for heat and air or what. Are they covered with an insulation blanket? Are they just pressed end to end with no internal connector? Foil tape may work but with details we may be able to give you a better solution.
#2
So this is for a dryer. I missed that the first time.
It is now illegal to use plastic ducting for dryers. Too many fires caused by them. Tell the landlord it is unsafe and needs to be replaced.
it's basically a metal like hose and a plastic type hose
#3
If you have any more questions post back. Ideally the dryer should be against an outside wall and vent directly outside. I get the impression from what you write that is not what your situation is.