If using a Custom Shipping Option you can set flat fee shipping prices based on either the value of the products in the cart or the weight of the products in the cart, special shipping price if the cart contains certain products, etc.

To set custom shipping options... Shop --> Settings --> Shipping.

On the Settings tab you indicate whether you are using just Custom Shipping options or whether they are to be used in conjunction with Flat Rate or Live shipping options.  When using Custom Shipping with either Flat Rate or Live, all shipping options that apply will be presented to the customer at checkout.

All fields are required and Custom Shipping options only appear to the customer if they meet ALL variables in the setting (ie, cart value, cart weight, zip, States, Countries, and Products).

Name/Label - is what the customer will see as their shipping option.
Cart Total Range - is the needed dollar value of the cart, this is a required field. If not using, set the range to something exhorbitant so that this does not interfere with the other options you are setting.
Cart Total Weight -  is the total weight of the products in the shopping cart, this is a required field. If not using, set the range to something exhorbitant so that this does not interfere with the other options you are setting.
Shipping Price - this is the shipping fee the customer will pay this price.
Shipping Speed - this is only meaningful for Amazon FBA orders and corresponds to Amazon definitions for shipping speed.
Include/Exclude Zip - if not using, radio button should be set to Use Exclude List and the list should be null.
Include/Exclude States - if not using, radio button should be set to Use Exclude List and the list should be null. States are entered using their 2 digit abbreviations.
Include/Exclude Countries -  if not using, radio button should be set to Use Exclude List and the list should be null. Country codes are specified as the 3 digit ISO codes.
Products - Should be set to Applies to All Products if not limiting to specific products. When set to selected products, if the customer has ALL of the listed products in their cart and they meet the other filters (above) they will be presented this shipping price. To add a product to the list, start typing in the search box and click on the product when it appears in the popup below the search box.

note: Custom shipping will override a flat fee shipping price on a product if applicable.  Any active shipping options that apply to an order will be presented to the shopper at the time of checkout.