Are you specifically talking about Adobe Flash, or do you actually mean a "splash screen" rather than a "flash screen"? A splash screen is simply a form like any other. It can display Labels, PictureBoxes, etc, just like any other form. The simplest option for animation on any form is to display an animated GIF in a PictureBox. You would do that the same way as you would for any other Image.
Creating the GIF in the first place would be done outside VS and is therefore not really a topic for discussion here. You can find various tools on the web, both free and commercial, that will create animated GIFs for you.