Integrating FO with Amazon

If I am to integrate with Amazon how would anyone suggest to do this?
E.g. forward Sales Invoice/Sales Order Confirmation or Import Sales Order

I know that we can use data management to export to BYOD but this doesnt seem to be best way.
Can anyone suggest what may be the best way?

Your first step is collecting functional requirements and thinking about non-functional requirements (performance, reliability etc.). It’s impossible to say what’s the best way for your needs before understanding your needs.

Then review integration options of both systems. You forgot to mention your version of AX, but the remark about BYOD suggests that it’s D365FO. D365FO surely has many more options than just BYOD, such as OData services, and it can call anything you’re able to develop (such as reading messages from Azure Service Bus).