Amazon offers a number of channels to sell via Amazon, but only the "Professional" Amazon Seller Account is supported by an API that can integrate with ShippingEasy. Amazon has more information about the "Professional" Seller Account on their website.
The "Individual" Amazon Seller Account is not supported through an API so unfortunately those orders cannot be pulled into ShippingEasy.
Another thing to note is that the Amazon Web Store Platform is not currently supported through an API either, so orders from a Web Store cannot be pulled into ShippingEasy.
How to use Amazon with ShippingEasy
How to: Integrate Amazon with ShippingEasy
Video: Integrate Amazon with ShippingEasy
If I use Fulfillment by Amazon, will that cause issues within ShippingEasy?
Why do my Fulfillment by Amazon orders not sync with ShippingEasy?