You would want to write a trigger on the FeedItem object and then use a callout to post the data to Amazon. I would start by doing the Apex Integration Services Trailhead [1] and then take a look at this blog post [2] for more information on multipart form uploads to Amazon.
[1] https://developer.salesforce.com/trailhead/module/apex_integration_services
[2] http://blog.deadlypenguin.com/blog/2016/02/16/amazon-s3-attaching-a-file-in-salesforce/