Amazon orders that are "Fullfilled by Amazon" are part of the Amazon Fulfillment Network (AFN), which means they shouldn't be fulfilled using any third-party system-- including ShipStation.
For search visibility and reporting purposes, you can check a box to import those orders into the "Pending Fulfillment" or "Shipped" statuses. Note that orders imported this way count toward your ShipStation subscription plan's shipment limit.
You can find this checkbox in the ShipStation settings for your Amazon store:
Head to your Account Settings (the gear icon in the upper right).
Next, select Selling Channels and then Store Setup from the sidebar on the left.
From here, click Edit for the Amazon store that needs the AFN orders to import for visibility and reporting purposes.
Under the Store Information sub-tab, scroll to the "Store Settings" section and check the box for the "Import FBA Orders."
Don't forget to Save Changes when you're done!
*Note that this is option is only available for US-based Amazon.com accounts.