With your object, first attach a swivel exit animation, and set its timing to be "slow" - 3 seconds.
Then attach a "disappear" exit animation, but set it's delay to be .6 seconds, and set it to "start with previous", so that it starts at the same time as the swivel, but doesn't do the disappear until .6 seconds.
This means that the swivel will start on a click, but then disappear entirely when it gets to the sideways on point, which is at the .6 second mark.
So that is the top card disappearing.
For the "back", you use a swivel entrance, but it needs to be hidden from view until it has reached the right point in the swivel. You can't combine entrance animations, so you need a third object that sits between the "front" and the "back" object. This should be the same colour as the slide background, have a "disappear" animation, set to start at the same time as the swivel for the "back" object, but with a delay of 2.5 seconds.
So the swivel starts for the "Back" object, but it isn't seen because there is an opaque object over the top of it. At 2.5 seconds, the opaque object disappears and you see the end of the swivel for the "Back" object, which at 2.5 seconds appears to be when it is sideways on.
You'll need to start the "Back" swivel animation prior to the first object, because it appears to do three turns before completing. So you want it to appear when it is sideways on in the last revolution, and then have the Appear animation kick in then, so that the previous object's Disappear and this ones Appear coincide.
If you get the timing right, it should look like the object flipping over.