It does depend on the document a bit, but basically it's just about one second, maybe a smidgen more. When you push the page turn button, nothing visible happens at first for about half a second. Then it looks very briefly like the page is inverting the black and white colors. I.e. if it's a page with regular text, you will see all the gray background turn black and see what sort of looks like white text. It's too fast to tell if it's the exact inverse of the previous image or if it includes part of the next page, but probably that's a step that clears the previous image. Then it immediately inverts again and the whole next page appears.
If you want the timing breakdown of the pause, imagine counting 1,2,3,4 to cover a one second period of time, and then the breakdown is like this:
1: Push the page turn button
2: Wait... still no apparent change in the first 1/2 second
3: Inverted flash happens all at once at the count of "3"
4: The next page appear at the count of "4"
You might think that the way it doesn't do anything for the first 1/2 sec is bad, but actually it's an advantage. Multiple people told me that when they read, they get accustomed to pushing the page turn slightly in advance as they finish reading the page. So that really only leaves 1/2 second without text available for reading. It feels a little sluggish, but in my opinion not enough to be a problem for most people. On the other hand, if they could speed up the E-ink display product, that would obviously be a nice improvement.