There is a way to fold hoop panniers flat ^^
(Steps with pictures)
The first key is at the beginning, right hand thumb toward inside to body, left hand thumb toward outside from body!
then start to turn your hand to REVERSED way, right hand turn outside, left hand turn inside to body.
your thumb should turn...totally a 360 circle..
finish the turning part.
neaten the fishnet and lining..
By the way, the hoop are all adjustable in circumference (by a small plastic pipe at the tip), it can be shorten or larger for less or fuller volume.
If you prefer to wash the hoop petticoats, you may need firstly remove the steel hoop from the skirt, them wash the skirt part.