How do I set up a shipping method that charges a flat rate for the first item and a lower flat rate for each additional item?

Products that need the flat shipping rate should have a weight of 1 in the associated pricing engine.  You would then create a non-integrated shipping method.  The non-integrated shipping method would have a handling fee equal to the initial flat rate minus the cost of the later flat rate. Then a per-unit charge equal to the later flat rate.

For example:
1st item flat rate = $10
2nd item flat rate = $8

handling = $2
per-unit charge = $8

1 item = weight of 1 = 2 + 8 = $10
2 items = weight of 2 = 2 + 16 = $18 (10 + 8)
3 items = weight of 3 = 2 + 24 = $26 (10 + 8 + 8)

 

Related article: Ch. 017. Creating Shipping Methods