Is there a app or software to do random photo selection on iphone?
The built in slideshow would work to set the order of photos to random if you've already classified the photos into an album. Just set the delay to a while and remember to re-choose the album to re-seed the randomness if you choose to repeat the selection.

If you need to classify photos on the go, you can use the iPhoto app to import / sort / add / remove photos from a group and then set up your random slide show for the ordering of them at random.

As a bonus, you can play music if desired while you set things up. I don't know of an app to provide your slot machine animation but perhaps someone can find just that app on the store for you.