The Soundboard is not an app that you must download from the various app stores.  It is simply a website that is optimized for mobile.  However, Safari on the iPhone allows you to create a link to any website on your desktop for one-click access, just like an app.

Visit the Soundboard with the link provided to you, then click the box at the bottom with the arrow pointing up.

Once you click the box, there will be a number of choices.  Click the one that says Add to Home Screen.

Once you've clicked that, you can name the link whatever you'd like, and you now will see it on your desktop.  This button will bring you back to the Soundboard with one click.