start collar mastic sealed to plenum.
inner liner mastic sealed to start collar.
insulation jacket and insulation brought in
contact with plenum. mastic sealed insulation
jacket to plenum.
lock ties are often used to hole insulation
jacket and insulation in place.

either paint on mastic or mastic tape can be used.
paint on mastic takes longer, as mastic has
to dry.
mastic tape is more expensive, but good long
lasting seal. because it doesn't have to
dry, it goes quicker.

I use Hardcast brand 1402 mastic tape.
silver with sticky gray (mastic) backing.
costs about $30. per roll at hvac supply.

foil tapes are not strong enough. just like
duct tapes, they fail quickly in extreme attic
heat.

best of luck.

Looking @ it closer, I see a gray sticky material on the inside of the flex and the tape has a grey sticky backing (tape is metallic). It looks like they used the right materials but for some reason the duct still fell off (metal was dusty?).

inner liner connected to supply box,
same install for plenum install
don't know how to do multiple pics
so outer liner pic to follow

and last.