You just need to Synchronize.
Open the Dictionary and Flashcards app and include your trainchinese account data into the settings (My Account/Upgrade - > Account details), then tap on the top right button (on iOS an orange button, on Android "Update Cards").
Then all the data is synchronized. You can use several devices and the website to train. Just make sure to use the same account and also to "Synchronize" before changing the device.