Although you have given us very little information (e.g. we know nothing about your computer nor even the exact version of Photostory that you are running!) I assume you want to create a slideshow, using Photostory, in which the order of the displayed pictures is random. Is that correct?
If it is, I don't think you can! The process of exporting the finished file from the program inevitably "burns in" the order in which the images are viewed. Playback of that file, whatever its format, is bound to be linear, I think.
Like the OP, I would like to be able to have pictures I first load in to Photostory automatically randomized prior to burning a final copy. So to be clear, when I upload photos 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, I'd like to click a button and have Photostory re-order to something similar to 4, 1, 9, 5, 7, 8, 10, 2, 6, 3.
By the way, I have a Windows 10 i7 laptop with 16 gigs of RAM. I am currently running Photostory 2014. I'd consider an upgrade if just this one feature were added. And I do understand that I can drag and drop pictures. But with hundreds of pictures, I'd like to have an automatic way of doing this. Thank you.