There’s already oEmbed support in WordPress, so you can simply paste any Soundcloud URL in a WordPress post and it will load the SoundCloud player. See http://codex.wordpress.org/Embeds
In any case, Post Formats are not something that can be added to–they are fixed and controlled by WordPress itself.
I could create a new Custom Post Type and include that with the theme, but that’s outside the scope of what I plan to do with this theme. You’re more than welcome to do so in a child theme, however.