The good news: you can get it running on the free tier (with a tiny instance).
The bad news: it's stuck on Elasticsearch 1.5.2 and dynamic scripting (Groovy) is disabled.
http://docs.aws.amazon.com/elasticsearch-service/latest/developerguide/aes-limits.html
Authentication: the safest option is to create a brand new IAM user (using the tool at https://console.aws.amazon.com/iam/home?region=us-east-1 ) with its own access key and secret key. Then when you create the Elasticsearch instance you can paste in the following IAM string: