Make sure your thumb is moving along a curve. If you flick it straight, the card may flick the wrong direction or fail to flick.
Your thumb and the grip of your fingers should apply moderate pressure. Adjust if the card keeps slipping, or buckles too far to move easily. Speed up the movement of your thumb for better results. Rotate your wrist as you flick for additional force.
If you’re not confident you can catch it, flick the card directly at a spectator instead when you perform. This won’t derail the act in the same way dropping the card could.