When my DD was 3 we played those kind of card games. Once I was done dealing, I'd fan them out facing away from me in a tight pattern, so all the numbers were visible but the bottom right corners all overlapped. I also learned to focus away from her cards when she would inevitably expose them.
That worked for her, but if she was still having an issue, I'd probably give her something like a board game box and let her lay them all in there. She could lay her cards down flat against one part and have the other part vertical to screen them from view.
I think a chip clip would probably damage the cards. It'd have to be one with soft pads at opposite sides of the compression point, and most of them have hard, serrated teeth.
