I know that many in our profession are scared by this idea because they say 1) staff and adults won't be able to find things and/or 2) things will be out of order. My response to this....
Many may think that spine out display is easier for staff and adults, but it's definitely not easier for or appealing to kids and, to me, the #1 goal for children's libraries is to connect kids to the collection. And, according to several libraries who have implemented face out, flip-through shelving, it can be easily accessible to adults too. The key is to think about the system you set up, how you process the materials, etc.
Over the past several months I've been doing a great deal of research on and analysis of picture book and other children's collections. I've found that with some weeding (sometimes some pretty significant weeding) and transitioning to flip-through shelving, circulation of materials is going up anywhere from 20 - 40%. If you're looking for some good examples to share with decision makers, the Indian Prairie Public Library in Darien, IL has had great success. See their YouTube video for more information. The Frankfort Public Library District in Frankfort, IL has also reported significant increases in circulation. Several of my clients are also in the process of transitioning. A few have already, in a few short months, seen the positive results of both weeding and flip-though display.
When looking for flip-through / face out / bin shelving, there are many products on the market to choose from. Biblomodel shelving is one of many good options. Both Indian Prairie and Frankfort use this type of shelving. In addition, I've put together a picture book shelving resource to show you a few others.