Here is a simple hack that took me a while to locate, so here is a post to document…

The PayPal cart and buy now buttons allow you great variety in shipping, but how do you charge a flat rate for shipping per order? It isn’t obvious.

Add the following line of code to your “buy now” or “add to cart” button forms:

<input name="handling_cart" type="hidden" value="2.00" />

The value above is the flat rate you want to charge per cart in dollars.

Update:
The above works as long as people are ordering one type of product. If more than one product is added to the cart, the handling_cart value for that product will be added also. If someone knows how to get true per-order flat rate shipping implemented, let me know.