If you are using the FatFreeCart.com cart, first bear in mind we provide that on a strictly do-it-yourself basis with no support whatsoever (that's a major reason it's free :^), so you'd be responsible for figuring things out, setting it up, troubleshooting any issues, etc.
That said, I can at least confirm that FatFreeCart does not support per-order flat-rate shipping; it only supports per-item flat rates. If you decide to upgrade to E-junkie cart (aka "FatFreeCart Pro"), that would include email-/forum-based tech support and does indeed have much more flexible shipping calculation options (including per-order flat rates) explained here:
http://www.e-junkie.com/ej/help.shipping.htm