Local ffmpeg output to S3 Bucket
You can:
Mount the S3 bucket using S3FS FUSE and then you output directly to it.
How to Mount S3 Bucket on CentOS/RHEL and Ubuntu using S3FS
Segment the media for HTTP streaming and upload each segment and playlists using the S3 API and a script of your choice.
I'd go with 1 for a live stream.
It could be late to answer this question, but I think this may be useful for others.
You can use this method to write output file to your S3 server.
ffmpeg -re -i in.ts -f hls -method PUT http://example.com/live/out.m3u8
Read more in https://ffmpeg.org/ffmpeg-all.html#hls-2