The backhand flip is like a mini loop. It all happens over the ping pong table so you can't have a big back swing. Again, it is important to keep your body well balanced. Drop the table tennis racket a little before contact and brush over the ball with a crisp, quick motion. This is the contact point. Be sure to give it enough forward momentum.
The backhand flip, you have to use a lot of wrist. You have to prepare with your body in a good position that you can make your backhand flip and with wrist you can make direction change in that moment. Wait for the ball when it's in highest position. Then you can make your backhand flip hard and deep.
The wrist action is the most obvious requirement but an important factor, that makes a huge difference in the quality of the flip, is the rotation of the whole arm. The elbow turns downward on contact. This is what gives the ping pong ball the necessary forward drive.
As with all short balls that require you to step in and reach over the table, make sure you recover immediately so you can't get caught off balance by a long ball.