I love this technique used to create this Owl:  http://cakecentral.com/g/a/3288743/owl-and-bird-cabin/

The problem I have is the fondant drying flat - it tends to buckle and curl around the edges and picks up the slightest flaw in both the wax paper & parchment paper (flaws, wrinkles I can't see).  I do not have metal cookie sheets I have Pampered Chef stones so I am not sure if that has anything to do with it.

Any ideas or suggestions as to how I can get a nice flat piece of fondant?

Lay your fondant pieces on a piece of foam sponge to dry.  Air circulates all around, so you never have to turn the piece over and there are no flaws to pick up.

You can find large pieces of foam in craft/fabric stores where the chair cushions and batting is.

Beautiful!  thank you!

I bought the plastic that is used for needlepoint to dry my fondant on. It has holes for air circulation. Are you rolling your fondant too thin? HTH