Yes, this is a common workflow to automate order fulfillment.
The general flow is:
1) Add the FBA fulfillment service to Shopify.
2) Mark your Shopify products inventory to be managed by FBA.
3) Set up the shipping rate to match Amazon's, and match product SKU's in Amazon / Shopify.
Here's a step by step guide to achieve that: https://speedboostr.com/automate-order-fulfillment-on-shopify.