How close is this in-joist duct that you are constructing to the HVAC equipment it is connecting to? And how far is the output of the supply from the exit of the room?
I think the in-joist duct silencer may not be necessary at all and in fact can be a bit detrimental, as Ted mentioned. If you have an in-joist silencer constructed of nothing but hard surfaces directly attached to the structure, you are essentially building a drywall "drum" that has the disadvantage of sound getting transferred (and possibly amplified) into the floor above . . . and all done in the name of capturing sound trying to escape the room through the HVAC.
If you are not too far along in the process, I would not construct the in-joist silencer and just run the flex line as normal, especially since you have double drywall above and a shell with clips and double 5/8" with Green Glue yet to come.
If you think of how difficult it would be for sound to enter through your HVAC supply and navigate all of the twists and turns contained within 19' of flex line to get out of the room, you can see where building a "drum" of drywall behind the shell may not be the optimal tradeoff.
Interested to hear your thoughts.