I want to create an effect in which the entire Stage effectively zooms really big and then I can transition into another scene. How do I zoom the Stage for the user?
Using the Zoom tool to zoom the Stage will only affect your workspace. What you need to do is scale everything on the Stage by using a tween. This can be difficult because you might have several layers. You can solve this a few ways. If you created everything inside one large movie clip, you can just scale an instance of that clip in the main scene. If you've already built everything in the main Timeline, you can effectively take a snapshot of the last frame and then place that inside a clip that gets scaled. To do this, go to the last frame and copy everything on the Stage from all layers at once. Insert a blank keyframe in a new layer and then paste it in place. To make sure the clip you're about to make doesn't include any nested looping movie clips, while everything is still selected, use the Properties panel to set everything to Graphic symbol set to Single Frame, 1. While everything is still selected, convert to symbol (and make this a movie clip). Then it's just a matter of inserting more frames for the tween where you scale this new clip.
Are there any good resources for more animation techniques in Flash?
By now, you have most of the technical skills to execute anything in Flash. Studying other Flash books (there are several fine ones) probably won't help you as much as studying traditional animation. With a little refinement, you'll be able to do anything you have clearly defined. If you want some ideas, though, watch animations and movies and study the masters who came long before Flash.