HVAC duct in a Double Stud Wall

How did you guys get the ductwork across both the inner and outer leafs of double stud wall assembly without having the flexible duct act as a flanking path between the two leafs (thereby negating the benefit of having 2 separate leafs in the first place)? My understanding is that insulated flex duct will not act as a conductor like a solid metal pipe would, but I am not 100% sure of this and want to make sure I plan this out right. I am designing a small practice/jamming room that I will be building myself. I have read through this forum and Rod Gervais book. On page 123 of his book (figure 7.3), he shows a side view of an HVAC system entering a double stud wall studio from outside the studio. But he does not show how the ductwork actually goes from one wall to the next. So any help will be appreciated.

I dont think a Flex Duct will actually be a flanking factor, however, you must create soffits for it in both sides, meaning, the penetration itself will be covered and sealed by this soffit

I have recently read that if the duct requires a 4" diameter hole, to drill the hole with a 4 1/4" diameter and then seal the edges of the hole with acoustical caulk in order to help prevent any vibrations from the ductwork from transmitting to both leafs in the double stud wall. I was wondering if anyone else had any experience with this. The room I am designing actually is too small for soffits to be used inside the room. I do plan on using a soffit outside the room, but I want to be careful to avoid inadvertently creating triple or quadruple leafs with the soffit panels.

I dont think a Soffit would really create a 3 or 4 leaf effect at all, the surface is not something to worry about, and it something that has to be done. so you live with it The fact itself about creating big holes on your leafs is a mess itself, so you are obviously loosing some STC numbers there, but thats why you need to create the better enviroment ever, because you ARE making holes later, for electricty, HACV, doors and windows, etc

Ideally you'd run the duct through a soffit muffler to attenuate much of the vibration prior to letting it leave the protected envelope of the inner studio walls / ceiling. Might look something like this: