In shipping rules "Flat" just means the flat amount you've entered for that rule, it doesn't call up the USPS flat rate packaging prices. Shipping rules also don't scale up automatically for orders that fall outside of any quantity range that you set, if you create a rule that applies for orders of 1 to 3 items it only applies to orders of 1 to 3 items.
You can still get what you want without a lot of work though, just use packaging costs instead of shipping rules.
Keep your product settings as they are, and on the first screen at Seller Admin > Edit E-junkie Cart Shipping Settings set the price of the flat rate box you use in the Cost column for the Regular Box.
We'll apply that cost for every Regular Box that needs to be used for an order, and that will scale up automatically based on how many units are ordered and your packaging capacity settings. So in this case, the cost for a Regular Box is applied for every three items ordered.
Once that is done press Next to reach the Shipping Rules screen and just delete the rules you've created there and you are done. You won't need to use Shipping Rules at all. You also don't need to worry about weight settings on any new products either, since this is working specifically on the type of package you are using and the number of items that can fit in it.