Accessible Kindle requires you to be logged in to your Kindle account, as Kindle requires that. You can log in by clicking Login and Info on the first page (below the Kindle button).
You can go to the Utilities page and select Zoom In or Zoom Out to control the size of the pictures, and the number of pictures that will be shown in each page.
On some devices, you will need to zoom out, in order to make the two columns view available. To do that select Utilities and Zoom Out, until you get to a level which allows two columns view. You can than select a larger text size (in the Reader Options) if needed.
It all depend on the way you exited the app, last time you used it. If you exited using the Exit button on the Menu, you will be taken to the Library next time you open the app. If you exited using the Exit button on the Reader Page, you will be taken to the Reader Page next time you open the app.