I had the same problem with samples. Purchased books would show up in the Archived Items list, but samples would never appear. Here's what I figured out.
After the latest Kindle app update, I had to log in again. This apparently created a new registered device. To fix this, go to the Your Account page on Amazon.com. Under Digital Content, select Manage Your Kindle. In the section named "Your Computer and Other Mobile Device(s)", you should see a device named "2nd Android" or something like that. This is actually your current Android phone. Deregister your previous Android device name to avoid confusion, and rename the new one to something meaningful by clicking the Edit Info link.
I couldn't find any history of requested samples, so you'll need to go back to the individual book pages and request another sample. Make sure the Deliver To menu (below the Send Sample now button) is set to your current Android device name.