You're giving too many degrees of freedom to the cards.
Notice that the packet is bent with the index in the middle: that allows the cards to obtain an angular momentum, in addition to the momentum provided by gravity when you release the cards, and that causes the cards to flip around the front finger.
Get rid of the pressure in the middle, and just let gravity do the work while gently releasing with the thumb, all the extra actions should be aimed at controlling the direction where the cards are falling.
I recommend starting with a narrow gap between the packets, you go too high!
Then when you get the flow of dribbling the cards right (which you can tell also by sound), you can get the packets a bit far away.
Last point: since the cards are released one after another, one mistake may collapse the form. Releasing the cards as individual as you can, in a steady manner, will help the overall structure, while having clumps while you dribbling will cause to have "heavy" packets which will dictate where the following cards are going to land.
If cards flips in one direction, the hand should slowly move to balance the non-parallel motion of the cards.