Duct 'liner" goes inside, wrap goes outside.
My house duct trunk lines have sound liner. The old style black fiberglass. System is VERY quiet. I can't imagine that the foil faced stuff would absorb much. I work in the trade, but I've never seen anything with a foil lining for inside.
Like others said, even a short section of 'flex" on the branch lines helps a bunch. I used 12" of flex on each branch. Flexible connections [old guys call them canvas connections] on the unit itself help a bunch too, both supply and return.