Personally, I would setup the canvas to the dimensions I required and begin designing in photoshop (layer from layer) the images that you want to animate, they should be on their own layer so that when you setup the animation process you can hide/unhide each layer. Now, for the blending process I would suggest that you
google a little to find how to blend images because the example you posted is very poor.
Experiment a little and persevere with this because it really is a simple process to create something like the example you posted, infact, I'm sure you could create something better.
If you require for the animation to flow only once, ensure that the animation window can be viewed and in the bottom left you will see an arrow with the text
Forever next to it. Click that and select once.
Once you have everything finished and happy with your logo goto
File >>
Export and select
Macromedia Flash swf and finalize your settings to your preference (quality preference, background colour preference etc).
If you are wanting the navigation menu (as posted in the example) you'll need to have knowledge and be able to slice the images which you can easily find tutorials through googling. It is an easy process it just requires a little perseverance.