I 'hang' them on their chains in my closet - so basically I put a ribbon (usually the one that comes with the chanel box) through the chains and then tie the ribbon to the bar on my closet.
I like storing it this way cos then I don't worry about the quilts becoming flat.
I wonder if the chains will get overstretched though.
How do you store your flaps?
I'd be wary of storing them like this. It makes sense as the chain will never mark the leather but it pulls the leather out of shape. I purchased a pre loved that had been hung by the strap and the leather has become quite pointed on the top of the flap not rounded as the shape should be. Luckily it was calf leather and with a bit of TLC it has improved. I think lambskin would have wrinkled when coached back into shape. The bag was less than 2 years old

I've now made my own felt dustbags were I can drop the chain down the front & back easily to store.
If you have the white Mademoiselle Chanel dustbag they do have the flap at the front for this.