there are many different terms, some of them more specific than the English "flashcards". Here are a few I found quite sensible, with some added explanation:
Most likely for children:
- 识字卡: A card for learning to read and write, with images on one side, and Hanzi on the other
- 识图卡: A "remember-pictures-card", the same as a 识字卡
- 方字: "square characters", word cards for teaching reading
- 教学卡片: A "teaching" card, so it's written from the perspective of the publishing house selling prepared learning cards to students/pupils
- 抽认卡: A "take out-recognize" card, which is how it should be for flashcards, perhaps a more informal term
- 闪卡: From "appearing very briefly", which could be a semantic (not phonetic) borrowing from the English "flashcards"
- 闪示卡: A "briefly-show" card, perhaps the original word that was shortened to the form above
- 字卡: A Chinese character flashcard
- 生词卡: A vocab flashcard
I'm sure there are more, so one can learn from this that the Chinese are used to studying diligently with the help of flashcards.