The equivalent in Kindle to folders is collections. Usually you can create this on the ebook reader yourself.
This Kindle help document https://www.amazon.com/gp/help/customer/display.html?nodeId=201733490 indicates that there is a cloud component to collections on later devices, but I don't know what this means for kindle apps.
For the Android Kindle app's main screen, when you keep holding down on the ebook title,a + option will appear which allows you to add to collections.
UPDATE: https://www.amazon.com/gp/help/customer/display.html?nodeId=201715640 "Note: Collections created on devices or apps that support Cloud Collections cannot be imported to devices and apps that do not support Cloud Collections. Any existing collections you’ve created on non-supported devices will not change and will not be available in the Cloud."