If you use the packaging system instead of our normal shipping rules you will be able to apply specific flat rates to specific items, and have those rates increase based on the quantity ordered.
Each product you sell can be designated to a particular packaging type, along with a capacity setting that controls how many units can fit in a single package. Different items that are assigned to the same package type can share that package as long as they don't completely fill it.
The Tube package type has a unique feature that assumes any item which fits in a smaller tube can also be rolled into a larger tube, so all items in tubes will be combined in the largest tube.
This setup will allow you to assign different flat rates to different products, but it is an account-wide setting so it would apply for all possible locations and cannot account for some nearby domestic destinations having cheaper shipping options than others.
However, if you are also shipping internationally you can use the packages to establish your domestic costs and then use shipping rules to apply additional costs for far-off destinations.
In general I always recommend going for the simplest shipping setup that can cover your costs for materials/labor and shipping on average without replicating the exact cost for every possible situation. Simple setups are easier to enter and maintain as outside costs change and are also easy for buyers to understand as part of their purchase.