Sophia here from Shopify. Welcome to the Shopify Community!
Printify offers a couple options for setting up shipping, depending on your Shopify plan.
Printify's flat rates use the weight-based shipping settings on the Basic plan or Shopify plan. The guide in their help center details a few different examples of how you can configure these weight-based rates. Alternatively, you can set up flat rates based on price of the order rather than weight.
Printify's calculated rates can be added using the carrier-calculated shipping feature. This is included for all stores on the Advanced plan. Alternatively, this feature can be added to any plan for $20/month in addition to your current subscription, or can be added for free if your store is billed annually, biennially, or triennially as opposed to every 30 days.
Let me know if you have any questions about these options and I would be happy to help! If you'd like to add carrier-calculated shipping to your store or need to discuss anything else account-specific, our Support team can assist you via live chat, email, or callback. You can access these contact options by visiting this page: https://bit.ly/3cJkx8V.