One Corbin seat has the flap, another version has a 'plug' of upholstered foam in-place of the flap. Some have gel inserts. They usually have a label on the underside if they have the gel inserts. I use a Corbin, and I find it OK for my shape and weight. I tried one when I bought my bike at the dealer 28 years ago, the salesman made a big push to put me onto one but they weren't willing to cut me a $-off MSRP, and I used the OEM seat for many years. Later I bought one in good shape (Corbin gel) and have used it since. Any decent upholstery shop should be able to sew you a new cover. Changing the foam is a different matter. Corbin may offer a rebuilding service, or you might try someplace working upon bike seats like Sargent Saddles, in Jacksonville FL.
Sargent Cycle Products - Custom Seat Services - World Sport Refurbishing Services