There is no restriction on the number of files that can uploaded to Amazon S3 at once from Salesforce.


Using the "Upload Files to Amazon S3" option, you can upload a large number of files at once. Simply click the button, choose the necessary files from your computer, and upload them all at once. 




PS: View Drag, Drop & Upload Files to Amazon S3, a Salesforce AppExchange app for moving files from Salesforce to Amazon S3: https://appexchange.salesforce.com/appxListingDetail?listingId=a0N3000000B5ZPqEAN