Seeing as BRD's got Perform and the Yoshi has said that the dev team are interested in adding more in-depth emotes, I would like to suggest that AST's get the Deck of Sixty.
It isn't really mentioned much ingame but the lore book goes into more detail about the decks used in Eorzean divination (and play), the Deck of Sixty.
As the name implies, it is a deck of 60 cards, 6 Major Arcana cards (the cards AST use in battle) and 54 Minor Arcana cards, 6 suits to represent the elements (Crowns, Cups, Rings, Knives, Staves, and Irons) , each with 9 cards (Aces to Sixes, then Knaves, Lords, and Ladies).
Usually, only the 6 Major Arcana are used but the Minor Arcana can be used, depending on the user and what spread is being used.
I have two ideas for how this emote could work:
1) Using only the 6 Major Arcana cards, the user can choose between two spreads: the Trinity (a spread that only uses 3 cards) or the Dawn Cross (a spread that uses all 6 cards).
When the Spread's button is activated, large versions of the cards will appear in front of the user, face down, in the spread the user selected.
Then the user can activate a Flip button that will flip one card, in order based on the spread.
The cards can be either normal (facing the correct way) or reversed (upside down).
Once all the cards are flipped, they'll dissapear after a seconds. The cards will also dissapear if the user moves their character.
This option might need to be named something else, seeing as you're only using 6/60 cards...
2) Using all 60 cards, the user can place up to 6 cards on the ground and can flip them over one-at-a-time using a Flip button, in the order of when they were placed.
You can have the option of placing either a random card(s) or specific card(s) (via seperate buttons).
The cards can be either normal (facing the correct way) or reversed (upside down).
The cards will be placed in a location designated by the user (think like Shadow Flare, Sacred Soil, Assylum, etc).
Once all the cards are flipped, they'll dissapear after a seconds. The cards will also dissapear if the user moves their character.
With this option, the user can use their own spread.