Unless you have an iron-clad requirements document, that they can't change once you start work, don't bid a flat rate! Strictly time and materials.
If you want to keep them happy, they need to understand that changes are quite acceptable, but those changes will cost them money. That makes it in their best interest to make good decisions about what they want, and it means that you aren't left "on the hook" forever trying to support those changes at no charge.
-PatP