To upload files you have stored on S3, you can either make the file public or, if that's not an option, you can create a presigned URL.
To make your file public on S3, navigate to the file, right-click and select Make Public. After doing so, go to the Properties for the file, and the Link value can be used to upload to data.world.
If your file is private on S3, you still have the option to generate a presigned URL for sharing or uploading to data.world. First, you will need to install and configure the AWS CLI. Once that is in place, use the following command to generate the URL for each file:
aws s3 presign <S3URI> --expires-in <expireTimeInSeconds>
Where S3 URI is in the format s3://mybucket/myfile.