There is probably some physics variational problem there where the energy over a surface is being minimized subject to constraints – but probably you should just sew a model of a single chamber, stuff it the way you plan, and then measure the final dimension to get the change in shape. That probably would give you a good idea.
If the baffles are sewn through then the answer should be easy to estimate since by stuffing you in effect turn the to parallel lines on either side of the chamber into an oval and eventually a cricle. If this oval was diamond shaped (to first approximation) which will slightly *underestimate* the actual shrinkage in length, then I make the shrinkage percentage to be
squareroot( 1-(W/L)^2 )
where W it the thickness you stuff the baffle, and L is the original distance between the sewn through lines. The actual shrinkage should be a bit more, but this should be pretty good as a first estimate.
If you really stuff the baffle (not a great idea) itshould roughly circular when you get done, which sounds about right (though probably a bit extreme) then
r = 2/pi = 0.64
So is r is the shrinkage percentage perpendicular to the sewn-through baffles then
0.64 < r < squareroot( 1-(W/L)^2 )
Multiply either of these two number (real result probably somewhere in the middle) by the original length of the bag to get the final length.
If the baffles are really wide with respect to the thickness then you could use a rectangular approximation (where the down is mostly the same thickness through the whole chamber and then suddenly shrink to zero at the seams) and then you would have:
r = 1- W/L
Proofs left as a homework problem, but I can write them up if you need them.