If you are in the web chat you could just display the user list by clicking it’s button of course.
On the TMI (irc type) connect, you would execute:
/raw CAP REQ :twitch.tv/membership
Adds membership state event (NAMES, JOIN, PART, or MODE) functionality. By default we do not send this data to clients without this capability.
/raw CAP REQ :twitch.tv/commands
Enables USERSTATE, GLOBALUSERSTATE, ROOMSTATE, HOSTTARGET, NOTICE and CLEARCHAT raw commands.
/raw CAP REQ :twitch.tv/tags
Adds IRC v3 message tags to PRIVMSG, USERSTATE, NOTICE and GLOBALUSERSTATE (if enabled with commands CAP)
Twitch messaging interface (TMI) has it’s own API, but it’s not supported and can change at any time. You could request the list of active moderators from: http://tmi.twitch.tv/group/user/:CHANNEL/chatters
Again, This API is not documented or supported. It is subject to change without notice.