It won't be impossible. You basically want this github.com/meteor-factory/react-native-tinder-swi…

So from there you'd need to stack the tiles, from an array or similar. Then change the swipe directions and have a point for cutoff (where the tile gets dropped from the top view) - which is already there, just for a different direction.
The content of each card with animations will be trivial. Then figure out how to minimise the card and display something below it (if you want that bit) - this is the hard bit!

Hope this helped.