I haven't found that they flatten - quite the opposite in fact! I've had 2 that were a bit overstuffed and they didn't prove to be very popular. The best one I have is a Tuffie 'skin' donated by a friend (she kept the innards) and I restuffed it with a smaller duvet.
I've recently reorganised all my beds (I have a bed fetish it seems) and converted them all to same colour same size Tuffies (they made me some new skins). I have the wipe clean version and it's really hard wearing.
If you haven't seen a Tuffie before it's worth trying to find someone near you that has them for you to look at. The surface doesn't suit all dogs, mine like them covered, but even with that caveat I wouldn't choose anything else.
(Towelling cot sheets make handy covers if you get the Tuffie size right and you can have a look at
Orvis too - they have some very nice, but quite expensive, bed covers)