This is super simple to do in Hype. You could bring in an iphone image with the rectangular face of the phone cut out in Photoshop, brought into Hype as a PNG (or the thinner "frame" part of the screen content that will move or have animating graphs/charts, cut out). Put that on the top layer. You could also lay out all the content of the screen in Hype as well, or make them in Pshop or Illustrator and bring them in as jpgs and pngs, just put the content that doesn't move above the phone png, and on the left, leaving the cut out part where the animations happen uncovered.
Then, below the phone layer, make a rectangle the same size as that screen or of the animating frame (it could be slighltly wider the the screen width as the side bezel of the phone will hide it). Group that rectangle. Make the Content Overflow of the group hidden, meaning anything that goes outside of the boundaries of the group (same size as screen) will be hidden. This will act as the window through which the animation you'll create is seen.
Then, select that rectangle, and copy and paste it twice to duplicate it twice. Then, keep one of the three rectangles in the middle, visible through the cut out of the phone png. Move another rectangle to the right, and another to the left. Select those three rectangles, and group them. This group will be what you animate, changing the horizontal position with keyframes, to simulate the screens/frames sliding back and forth, as if by swipe.
To get the animations on the screens, select each rectangle, turn it into a symbol, then in the symbol area, you can make all the individual animations on them, animate position and opacity, the charts and arrows and whatever wiping onto the screen, changing color, pointing up, pointing down.
Lastly, make a circle on top, drop the opacity, and match it's left and right position animation to the left and right position animation of the group of 3 rectangles (now animating symbols), and you're done.