Sometimes you can just figure it out by counting. In your specific example a Dminor7 will contain a basic Dminor, which based on the minor intervals is D-F-A, plus the 7th which is the C. With enough practice, you can learn to count it very fast, or even learn it by heart without needing a flashcard.
I'm the kind of person who doesn't like memorising things, I prefer to learn the underlying rules and then count my way. Even when playing the guitar (which I completely suck at), I'm so bad at remembering chord fingerings that I sometimes have to reconstruct them.