There is some confusion because Curator 3 supported AWS ES, but Curator 4 & 5 do not. There are even some IAM credentials listed as options for client connections. These are currently available, but not able to be used. This may change at some point, so they remain at the ready until then.
Curator 4 & 5 require access to the
/_cluster/state/metadata endpoint in order
to pull metadata at IndexList initialization time for all indices. This
metadata is used to determine index routing information, index sizing, index
close), aliases, and more. Curator 4 switched to
doing this in order to reduce the number of repetitive client calls that were
made in the previous versions. Curator 5 uses the same method.
AWS currently has a 5.1.1 version of Elasticsearch.
Unfortunately, this version does not fully support the
/_cluster/state/metadata endpoint, which means that Curator cannot be used to
manage indices in AWS.
This thread (requires AWS login credentials) tracks the issue on the Amazon side.