I do not have the RS Guidebook Binder. I realize the OP asked specifically for someone who has used it. However, I have spent half my life in the publishing industry, so it is very simple. When you go to the online RS website store, take time to look at the inset pictures that show how to pull out the pages and install them. Also note that the instructions on the product page say "Our Guidebook Page Binder is designed to hold a set of pages up to ¼” thick." This means if you have a stack of papers/pages from the guidebook that is a lot more than ¼” thick, you will have to come up with another way.
To answer the question you asked, "Can I flip through the binder without all my loose pages flipping out?" Yes, if you don't greatly overload it. A slip-on spine like that is pretty secure, unless you overload it. Then, yes, pages will possibly come out as you are flipping through.
Per the instructions on the product page, also note that the binder is to be unloaded every day or so, back at your hotel room and a new set (¼”thick) of pages put into the binder for the following day, or make that, the next leg of your trip.
To be clear, the binders use is that, when you complete seeing an area such as, say, Bath and the Cotswolds, you are to remove those pages from the binder, and install a new set of pages for your next destination, let's say, install the sections on London that you will be seeing for the next day or two.
The Guidebook Binder is not meant to hold an inch thick stack of papers for your entire trip. It is obviously not designed that way. Large stack = yes, papers will fall out. Small stack (¼”) = no, won't fall out. Like any product, it helps to use it as directed. Hope this helps.