1. In Photoshop, select the path in the Paths tab. Use the "Load Path as Selection" option at the bottom of the window.
2. Go to the Layers tab and stroke the selection that you've made from your path.
3. Create the rest of the illustration in Photoshop with each element in its own layer.
4. Save the Photoshop file as a .ps file.
5. In Flash, import the Photoshop file. You will get a new window with some options. DO NOT select "Flatten Photoshop layers...". In Layer conversion, select "Maintain editable paths and effects". In Text conversion, select "Editable Text". In Convert layers to, select "Flash layers.
6. In the Flash timeline window you should see each of the objects from Photoshop in individual layers as it was in Photoshop. In the Library panel you will see a folder that contains all of the Photoshop elements.
Here is a simple introduction to path animation: How to Animate along a Path in Adobe Flash CS6 - For Dummies