The Trading Card Kiosk is a feature that will allow you to trade your repeated cards for gems. To enter, go to the machine room by selecting "Get more cards" from the Gift Board in the "Gems" section within the Shop. Once you're there, you'll see the "Album" and "Trade" buttons at the bottom of the screen. If you click on the latter, you will be redirected to the Trading Card Kiosk.
In the upper sector of the screen, you will see the amount of gems you have at the moment and also the number of repeated cards. In case you have more than 99 repeating cards, your amount will be shown as 99+.
Every 5 repeated letters, the Kiosk will give you a gem and you will have the possibility of making 3 trades every 4 hours. Once you reach all three trades, the Kiosk will display a countdown counter until the ability to trade again is enabled.