You can think of Flash Catalyst as a front-end for Flash Builder; it lets you lay out a project in Photoshop or Illustrator, import it into Flash Builder, and by assigning button and contents to states, make a Flex project. Flex is alternative, component-based way of creating SWF files, based on XML and ActionScript. You use Flash Builder (called Flex Builder before CS4) to manipulate the XML file that controls your project. Like Dreamweaver, it has a design view and a code view.
Flash is the traditional authoring tool for SWF files. It is timeline based, and traditionally you build your project in a design window. However, you can also use ActionScript with Flash, and it has faciliites for editing ActionScript files. Thus you can lay out your project graphically, but still have ActionScript code interact with the design elements.
They are sort of two different ways of doing the same thing, and it sort of depends on your perspective. If you like designing your whole project in Illustrator or Photoshop first, and then adding animation, Flash Catalyst and Flash Builder is probably the easiest way to go. If you like building your project in Flash, and pulling in elements made previously in Photoshop or Illustrator, Flash might be best, especially if you are used to working with animation timelines.
You could make flip books either way. With Flash Catalyst/Flash Builder, you would make your book with each page on a separate layer, with separate layers for "next" and "previous" buttons. Then you would import your PSD into Flash Catalyst, and assign each page layer to a different state. Then you would save this as an FXP file, and import it to Flash Builder to create your SWF file.
With Flash, you could bring import the same PSD, and assign each page layer to a different frame on the timeline, and use the buttons to move between frames.
But I would recommend that you do neither of these. I would recommend composing your flip book in InDesign, which has an SWF flipbook export option. Especially if your flipbook is designed like a book, with text and pictures (rather than just being a stack of images, for example), InDesign is set up for designing that sort of thing, much more so than the other products. Certainly you can do fancier animation sort of things with Flash or Flash Builder, but if you just need to flip between pages, InDesign is the way to go.
(And there's actually another option: you can design your book in InDesign and export it as an XFL file, which you can then import into Flash if you need to add fancier animations. )
Hope this helps,
Cross Design Group, LLC