I am a member of a public organization and I don't know how to access one of its repos with this.

It uses backbone routers, so try something like:

http://prose.io/#MyOrganization/my-repo

Worked for me.

Thanks. I ended up creating an issue for this and they mentioned a url like yours, except that I needed to append a master at the end, like @BHSPitMonkey suggested bellow.

Note: You also need "/master" at the end, or whichever branch you intend to work on.