How should I attach laminate foil dryer transition duct?
Duct Tape is good for a lot of things, except duct work!  It will eventually dry up and pull away from the heat in the vent.  

I would bend/dent one of the ends slightly so that it will fit easily inside of the other.  Then I'd secure it with proper HVAC foil tape, followed by a clamp around it.

Foil Tape


(source: homedepot.ca)  

Metal Gear Clamp


(source: homedepot.ca)