How to attach laminate foil dryer transition duct

I cannot say I'm a fan of the design of that vent - although looking at your other question, I'm rather surprised that lint is falling down into that gap. Possibly your fan is creating too much pressure, and it's backing up inside the vent at the 180 and thus air is escaping through the pushing some lint down into that gap, where it can get stuck.

If that's the case, then you might try installing a baffle inside the vent to force lint up far enough in the vent so that it has to go out the intended port, but which still allows water out. Like so...

Sorry, the color doesn't show well, but inside I've added a piece of metal running from just below the intake port to nearly the end of the angled portion of the vent, with a brace connecting it to the body to keep it stable. You can't see it but there should be drip holes at the point where the new plate hits the flashing for water drainage.

The idea being, lint flies in and cannot be forced directly down to the gap in question, but water will hit the tray, run back and go through the drip holes.

That or replace it with this

I went through this recently with my girlfriends dryer. Here is what I learned:

1. Her outside vent hood seeped rainwater, not much but enough
2. Her ductwork had a tiny amount of lint which soaked up the rainwater
3. Her “outside air” ducting for the all-electric central heat and air system damper didn’t open all the way causing the air to be drawn from and through the dryer ducting. The moisture in the ductwork lint was drawn into the clothing left in the dryer. (Her house is new and sealed very tightly!)

An additional clue something wasn’t right was indicated by the exterior vent for her kitchen cook stove - it “rattled” when the air conditioner ran!

Solution:

1. Replaced the dryer ductwork and exterior vent.
2. Disassembled dryer and cleaned entire dryer ductwork path
3. Cleaned the central air exterior air feeder pipe, cleaned the exterior dampener
4. Replaced furnace filter.
5. Cleaned a/c condensate pipe (ran hose water through it until it was no longer draining “green” water)
6. Fixed her supper on the Weber charcoal grill.

She is happy now. The dryer no longer “stinks” from the “wet lint” smell, her clothes remain dry and her air conditioner is working better.