Here's a Youtube video that shows a machine binding technique I want to try on my next quilt. It should result in an "invisible" binding similar to Harriet Hargrave's invisible machine applique, especially if you use invisible thread to do it.
http://www.youtube.com/watch?v=wprg5vzkuGw
Flatness in a binding occurs when the batting is not "filling" the binding enough. This happens when you cut the binding strips too wide. It has to do with the ratio of binding to batting that will be covered. The binding should be tight enough, when you turn it, that the batting completely fills the binding. Actually, I think it works better if the batting overfills the binding slightly. When you pull the binding to the front, the batting has to roll a little bit to accommodate; the binding feels a little short.