Before I use it in a quilt, I dampen the wool batting and then dry it in the dryer to shrink it. I don't know if that's what you're supposed to do, but it works for me.
I don't machine dry any of my quilts regardless of batting but drape them over something that's not necessarily flat like the back of the couch or a table (neither of which is big enough for the whole quilt). I think the "dry flat" is just so the quilt doesn't get stretched, since the weight of a wet quilt could cause stretching if you hung it from a line. If you can put it on a table (that won't get damaged from having a damp quilt on it) and the edges hang over a little, it'll probably be okay. Depends on how big the quilt is and how big the table is.
I'm guessing the quilts could be dried in the dryer and would shrink some, but maybe if you take them out before they were completely dry wouldn't be too much? Manufacturers are sometimes conservative with their washing instructions. I confess to hand washing a lot of "dry clean only" items.